1.
Unit prefix
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A unit prefix is a specifier or mnemonic that is prepended to units of measurement to indicate multiples or fractions of the units. Units of various sizes are formed by the use of such prefixes. The prefixes of the system, such as kilo and milli. In information technology it is common to use binary prefixes, which are based on powers of two, historically, many prefixes have been used or proposed by various sources, but only a narrow set has been recognised by standards organisations. The prefixes of the metric system precede a basic unit of measure to indicate a decadic multiple, each prefix has a unique symbol that is prepended to the unit symbol. Some of the date back to the introduction of the metric system in the 1790s, but new prefixes have been added. The International Bureau of Weights and Measures has standardised twenty metric prefixes in resolutions dating from 1960 to 1991 for use with the International System of Units, although formerly in use, the SI disallows combining prefixes, the microkilogram or centimillimetre, for example, are not permitted. Prefixes corresponding to powers of one thousand are usually preferred, however, units such as the hectopascal, hectare, decibel, centimetre, in general, prefixes are used with any metric unit, but may also be used with non-metric units. Some combinations, however, are more common than others, the choice of prefixes for a given unit has often arisen by convenience of use and historical developments. Unit prefixes that are larger or smaller than encountered in practice are seldom used. In most contexts only a few, the most common, combinations are established, for example, prefixes for multiples greater than one thousand are rarely applied to the gram or metre. Some prefixes used in versions of the metric system are no longer used. The prefix myrio- was a spelling variant for myria-, as proposed by Thomas Young. A binary prefix indicates multiplication by a power of two, the tenth power of 2 has the value 1024, which is close to 1000. This has prompted the use of the prefixes kilo, mega, and giga to also denote the powers of 1024 which is common in information technology with the unit of digital information. Units of information are not covered in the International System of Units, for example, in citations of main memory or RAM capacity, kilobyte, megabyte and gigabyte customarily mean 1024,1048576 and 1073741824 bytes respectively. In the specifications of hard drive capacities and network transmission bit rates, on the other hand, decimal prefixes. For example, a 500-gigabyte hard drive holds 500 billion bytes, the ambiguity has led to some confusion and even of lawsuits from purchasers who were expecting 220 or 230 and considered themselves shortchanged by the seller
2.
Fraction (mathematics)
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A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A common, vulgar, or simple fraction consists of an integer numerator displayed above a line, numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals. The numerator represents a number of parts, and the denominator. For example, in the fraction 3/4, the numerator,3, tells us that the fraction represents 3 equal parts, the picture to the right illustrates 34 or ¾ of a cake. Fractional numbers can also be written without using explicit numerators or denominators, by using decimals, percent signs, an integer such as the number 7 can be thought of as having an implicit denominator of one,7 equals 7/1. Other uses for fractions are to represent ratios and to represent division, thus the fraction ¾ is also used to represent the ratio 3,4 and the division 3 ÷4. The test for a number being a number is that it can be written in that form. In a fraction, the number of parts being described is the numerator. Informally, they may be distinguished by placement alone but in formal contexts they are separated by a fraction bar. The fraction bar may be horizontal, oblique, or diagonal and these marks are respectively known as the horizontal bar, the slash or stroke, the division slash, and the fraction slash. In typography, horizontal fractions are known as en or nut fractions and diagonal fractions as em fractions. The denominators of English fractions are expressed as ordinal numbers. When the denominator is 1, it may be expressed in terms of wholes but is commonly ignored. When the numerator is one, it may be omitted, a fraction may be expressed as a single composition, in which case it is hyphenated, or as a number of fractions with a numerator of one, in which case they are not. Fractions should always be hyphenated when used as adjectives, alternatively, a fraction may be described by reading it out as the numerator over the denominator, with the denominator expressed as a cardinal number. The term over is used even in the case of solidus fractions, Fractions with large denominators that are not powers of ten are often rendered in this fashion while those with denominators divisible by ten are typically read in the normal ordinal fashion. A simple fraction is a number written as a/b or a b
3.
Decimal
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This article aims to be an accessible introduction. For the mathematical definition, see Decimal representation, the decimal numeral system has ten as its base, which, in decimal, is written 10, as is the base in every positional numeral system. It is the base most widely used by modern civilizations. Decimal fractions have terminating decimal representations and other fractions have repeating decimal representations, Decimal notation is the writing of numbers in a base-ten numeral system. Examples are Brahmi numerals, Greek numerals, Hebrew numerals, Roman numerals, Roman numerals have symbols for the decimal powers and secondary symbols for half these values. Brahmi numerals have symbols for the nine numbers 1–9, the nine decades 10–90, plus a symbol for 100, Chinese numerals have symbols for 1–9, and additional symbols for powers of ten, which in modern usage reach 1072. Positional decimal systems include a zero and use symbols for the ten values to represent any number, positional notation uses positions for each power of ten, units, tens, hundreds, thousands, etc. The position of each digit within a number denotes the multiplier multiplied with that position has a value ten times that of the position to its right. There were at least two independent sources of positional decimal systems in ancient civilization, the Chinese counting rod system. Ten is the number which is the count of fingers and thumbs on both hands, the English word digit as well as its translation in many languages is also the anatomical term for fingers and toes. In English, decimal means tenth, decimate means reduce by a tenth, however, the symbols used in different areas are not identical, for instance, Western Arabic numerals differ from the forms used by other Arab cultures. A decimal fraction is a fraction the denominator of which is a power of ten. g, Decimal fractions 8/10, 1489/100, 24/100000, and 58900/10000 are expressed in decimal notation as 0.8,14.89,0.00024,5.8900 respectively. In English-speaking, some Latin American and many Asian countries, a period or raised period is used as the separator, in many other countries, particularly in Europe. The integer part, or integral part of a number is the part to the left of the decimal separator. The part from the separator to the right is the fractional part. It is usual for a number that consists only of a fractional part to have a leading zero in its notation. Any rational number with a denominator whose only prime factors are 2 and/or 5 may be expressed as a decimal fraction and has a finite decimal expansion. 1/2 =0.5 1/20 =0.05 1/5 =0.2 1/50 =0.02 1/4 =0.25 1/40 =0.025 1/25 =0.04 1/8 =0.125 1/125 =0.008 1/10 =0
4.
Binary number
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The base-2 system is a positional notation with a radix of 2. Because of its implementation in digital electronic circuitry using logic gates. Each digit is referred to as a bit, the modern binary number system was devised by Gottfried Leibniz in 1679 and appears in his article Explication de lArithmétique Binaire. Systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, Leibniz was specifically inspired by the Chinese I Ching. The scribes of ancient Egypt used two different systems for their fractions, Egyptian fractions and Horus-Eye fractions, the method used for ancient Egyptian multiplication is also closely related to binary numbers. This method can be seen in use, for instance, in the Rhind Mathematical Papyrus, the I Ching dates from the 9th century BC in China. The binary notation in the I Ching is used to interpret its quaternary divination technique and it is based on taoistic duality of yin and yang. Eight trigrams and a set of 64 hexagrams, analogous to the three-bit and six-bit binary numerals, were in use at least as early as the Zhou Dynasty of ancient China. The Song Dynasty scholar Shao Yong rearranged the hexagrams in a format that resembles modern binary numbers, the Indian scholar Pingala developed a binary system for describing prosody. He used binary numbers in the form of short and long syllables, Pingalas Hindu classic titled Chandaḥśāstra describes the formation of a matrix in order to give a unique value to each meter. The binary representations in Pingalas system increases towards the right, the residents of the island of Mangareva in French Polynesia were using a hybrid binary-decimal system before 1450. Slit drums with binary tones are used to encode messages across Africa, sets of binary combinations similar to the I Ching have also been used in traditional African divination systems such as Ifá as well as in medieval Western geomancy. The base-2 system utilized in geomancy had long been applied in sub-Saharan Africa. Leibnizs system uses 0 and 1, like the modern binary numeral system, Leibniz was first introduced to the I Ching through his contact with the French Jesuit Joachim Bouvet, who visited China in 1685 as a missionary. Leibniz saw the I Ching hexagrams as an affirmation of the universality of his own beliefs as a Christian. Binary numerals were central to Leibnizs theology and he believed that binary numbers were symbolic of the Christian idea of creatio ex nihilo or creation out of nothing. Is not easy to impart to the pagans, is the ex nihilo through Gods almighty power. In 1854, British mathematician George Boole published a paper detailing an algebraic system of logic that would become known as Boolean algebra
5.
Metric system
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The metric system is an internationally agreed decimal system of measurement. Many sources also cite Liberia and Myanmar as the other countries not to have done so. Although the originators intended to devise a system that was accessible to all. Control of the units of measure was maintained by the French government until 1875, when it was passed to an intergovernmental organisation. From its beginning, the features of the metric system were the standard set of interrelated base units. These base units are used to larger and smaller units that could replace a huge number of other units of measure in existence. Although the system was first developed for use, the development of coherent units of measure made it particularly suitable for science. Although the metric system has changed and developed since its inception, designed for transnational use, it consisted of a basic set of units of measurement, now known as base units. At the outbreak of the French Revolution in 1789, most countries, the metric system was designed to be universal—in the words of the French philosopher Marquis de Condorcet it was to be for all people for all time. However, these overtures failed and the custody of the metric system remained in the hands of the French government until 1875. In languages where the distinction is made, unit names are common nouns, the concept of using consistent classical names for the prefixes was first proposed in a report by the Commission on Weights and Measures in May 1793. The prefix kilo, for example, is used to multiply the unit by 1000, thus the kilogram and kilometre are a thousand grams and metres respectively, and a milligram and millimetre are one thousandth of a gram and metre respectively. These relations can be written symbolically as,1 mg =0, however,1935 extensions to the prefix system did not follow this convention, the prefixes nano- and micro-, for example have Greek roots. During the 19th century the prefix myria-, derived from the Greek word μύριοι, was used as a multiplier for 10000, prefixes are not usually used to indicate multiples of a second greater than 1, the non-SI units of minute, hour and day are used instead. On the other hand, prefixes are used for multiples of the unit of volume. The base units used in the system must be realisable. Each of the units in SI is accompanied by a mise en pratique published by the BIPM that describes in detail at least one way in which the base unit can be measured. In practice, such realisation is done under the auspices of a mutual acceptance arrangement, in the original version of the metric system the base units could be derived from a specified length and the weight of a specified volume of pure water
6.
International System of Units
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The International System of Units is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, the system also establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system was published in 1960 as the result of an initiative began in 1948. It is based on the system of units rather than any variant of the centimetre-gram-second system. The motivation for the development of the SI was the diversity of units that had sprung up within the CGS systems, the International System of Units has been adopted by most developed countries, however, the adoption has not been universal in all English-speaking countries. The metric system was first implemented during the French Revolution with just the metre and kilogram as standards of length, in the 1830s Carl Friedrich Gauss laid the foundations for a coherent system based on length, mass, and time. In the 1860s a group working under the auspices of the British Association for the Advancement of Science formulated the requirement for a coherent system of units with base units and derived units. Meanwhile, in 1875, the Treaty of the Metre passed responsibility for verification of the kilogram, in 1921, the Treaty was extended to include all physical quantities including electrical units originally defined in 1893. The units associated with these quantities were the metre, kilogram, second, ampere, kelvin, in 1971, a seventh base quantity, amount of substance represented by the mole, was added to the definition of SI. On 11 July 1792, the proposed the names metre, are, litre and grave for the units of length, area, capacity. The committee also proposed that multiples and submultiples of these units were to be denoted by decimal-based prefixes such as centi for a hundredth, on 10 December 1799, the law by which the metric system was to be definitively adopted in France was passed. Prior to this, the strength of the magnetic field had only been described in relative terms. The technique used by Gauss was to equate the torque induced on a magnet of known mass by the earth’s magnetic field with the torque induced on an equivalent system under gravity. The resultant calculations enabled him to assign dimensions based on mass, length, a French-inspired initiative for international cooperation in metrology led to the signing in 1875 of the Metre Convention. Initially the convention only covered standards for the metre and the kilogram, one of each was selected at random to become the International prototype metre and International prototype kilogram that replaced the mètre des Archives and kilogramme des Archives respectively. Each member state was entitled to one of each of the prototypes to serve as the national prototype for that country. Initially its prime purpose was a periodic recalibration of national prototype metres. The official language of the Metre Convention is French and the version of all official documents published by or on behalf of the CGPM is the French-language version
7.
International Bureau of Weights and Measures
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The organisation is usually referred to by its French initialism, BIPM. The BIPM reports to the International Committee for Weights and Measures and these organizations are also commonly referred to by their French initialisms. The BIPM was created on 20 May 1875, following the signing of the Metre Convention, under the authority of the Metric Convention, the BIPM helps to ensure uniformity of SI weights and measures around the world. It does so through a series of committees, whose members are the national metrology laboratories of the Conventions member states. The BIPM carries out measurement-related research and it takes part in and organises international comparisons of national measurement standards and performs calibrations for member states. The BIPM has an important role in maintaining accurate worldwide time of day and it combines, analyses, and averages the official atomic time standards of member nations around the world to create a single, official Coordinated Universal Time. The BIPM is also the keeper of the prototype of the kilogram. Metrologia Institute for Reference Materials and Measurements International Organization for Standardization National Institute of Standards and Technology Official website
8.
International System of Quantities
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The International System of Quantities is a system based on seven base quantities, length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity. Other quantities such as area, pressure, and electrical resistance are derived from these base quantities by clear, the ISQ defines the quantities that are measured with the SI units and also includes many other quantities in modern science and technology. The ISQ is defined in the international standard ISO/IEC80000, and was finalised in 2009 with the publication of ISO 80000-1. The 14 parts of ISO/IEC80000 define quantities used in disciplines such as mechanics, light, acoustics, electromagnetism, information technology, chemistry, mathematics. A base quantity is a quantity in a subset of a given system of quantities that is chosen by convention. The ISQ defines seven base quantities, the symbols for them, as for other quantities, are written in italics. The dimension of a quantity does not include magnitude or units. The conventional symbolic representation of the dimension of a quantity is a single upper-case letter in roman sans-serif type. A derived quantity is a quantity in a system of quantities that is a defined in terms of the quantities of that system. The ISQ defines many derived quantities, the conventional symbolic representation of the dimension of a derived quantity is the product of powers of the dimensions of the base quantities according to the definition of the derived quantity. The dimension of a quantity is denoted by L a M b T c I d Θ e N f J g, the symbol may be omitted if its exponent is zero. For example, in the ISQ, the quantity dimension of velocity is denoted L T −1, the following table lists some quantities defined by the ISQ. A quantity of one is historically known as a dimensionless quantity, all its dimensional exponents are zero. Such a quantity can be regarded as a quantity in the form of the ratio of two quantities of the same dimension. In the ISQ, the level of a quantity Q is defined as logr, an example of level is sound pressure level. All levels of the ISQ are derived quantities, B. N. Taylor, Ambler Thompson, International System of Units, National Institute of Standards and Technology 2008 edition, ISBN 1-4379-1558-2
9.
SI prefix
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A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or fraction of the unit. While all metric prefixes in use today are decadic, historically there have been a number of binary metric prefixes as well. Each prefix has a symbol that is prepended to the unit symbol. The prefix kilo-, for example, may be added to gram to indicate multiplication by one thousand, the prefix milli-, likewise, may be added to metre to indicate division by one thousand, one millimetre is equal to one thousandth of a metre. Decimal multiplicative prefixes have been a feature of all forms of the system with six dating back to the systems introduction in the 1790s. Metric prefixes have even been prepended to non-metric units, the SI prefixes are standardized for use in the International System of Units by the International Bureau of Weights and Measures in resolutions dating from 1960 to 1991. Since 2009, they have formed part of the International System of Quantities, the BIPM specifies twenty prefixes for the International System of Units. Each prefix name has a symbol which is used in combination with the symbols for units of measure. For example, the symbol for kilo- is k, and is used to produce km, kg, and kW, which are the SI symbols for kilometre, kilogram, prefixes corresponding to an integer power of one thousand are generally preferred. Hence 100 m is preferred over 1 hm or 10 dam, the prefixes hecto, deca, deci, and centi are commonly used for everyday purposes, and the centimetre is especially common. However, some building codes require that the millimetre be used in preference to the centimetre, because use of centimetres leads to extensive usage of decimal points. Prefixes may not be used in combination and this also applies to mass, for which the SI base unit already contains a prefix. For example, milligram is used instead of microkilogram, in the arithmetic of measurements having units, the units are treated as multiplicative factors to values. If they have prefixes, all but one of the prefixes must be expanded to their numeric multiplier,1 km2 means one square kilometre, or the area of a square of 1000 m by 1000 m and not 1000 square metres. 2 Mm3 means two cubic megametres, or the volume of two cubes of 1000000 m by 1000000 m by 1000000 m or 2×1018 m3, and not 2000000 cubic metres, examples 5 cm = 5×10−2 m =5 ×0.01 m =0. The prefixes, including those introduced after 1960, are used with any metric unit, metric prefixes may also be used with non-metric units. The choice of prefixes with a unit is usually dictated by convenience of use. Unit prefixes for amounts that are larger or smaller than those actually encountered are seldom used
10.
Short scale
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Thus, billion means a million millions, trillion means a million billions, and so on. Short scale Every new term greater than million is one thousand times larger than the previous term, thus, billion means a thousand millions, trillion means a thousand billions, and so on. For whole numbers less than a million the two scales are identical. From a thousand million up the two scales diverge, using the words for different numbers, this can cause misunderstanding. Countries where the scale is currently used include most countries in continental Europe and most French-speaking, Spanish-speaking. The short scale is now used in most English-speaking and Arabic-speaking countries, in Brazil, in former Soviet Union, number names are rendered in the language of the country, but are similar everywhere due to shared etymology. Some languages, particularly in East Asia and South Asia, have large number naming systems that are different from both the long and short scales, for example the Indian numbering system. After several decades of increasing informal British usage of the scale, in 1974 the government of the UK adopted it. With very few exceptions, the British usage and American usage are now identical, the first recorded use of the terms short scale and long scale was by the French mathematician Geneviève Guitel in 1975. At and above a million the same names are used to refer to numbers differing by a factor of an integer power of 1,000. Each scale has a justification to explain the use of each such differing numerical name. The short-scale logic is based on powers of one thousand, whereas the long-scale logic is based on powers of one million, in both scales, the prefix bi- refers to 2 and tri- refers to 3, etc. However only in the scale do the prefixes beyond one million indicate the actual power or exponent. In the short scale, the prefixes refer to one less than the exponent, the word, million, derives from the Old French, milion, from the earlier Old Italian, milione, an intensification of the Latin word, mille, a thousand. That is, a million is a big thousand, much as a great gross is a dozen gross or 12×144 =1728, the word, milliard, or its translation, is found in many European languages and is used in those languages for 109. However, it is unknown in American English, which uses billion, and not used in British English, which preferred to use thousand million before the current usage of billion. The financial term, yard, which derives from milliard, is used on financial markets, as, unlike the term, billion, it is internationally unambiguous and phonetically distinct from million. Likewise, many long scale use the word billiard for one thousand long scale billions
11.
Long scale
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Thus, billion means a million millions, trillion means a million billions, and so on. Short scale Every new term greater than million is one thousand times larger than the previous term, thus, billion means a thousand millions, trillion means a thousand billions, and so on. For whole numbers less than a million the two scales are identical. From a thousand million up the two scales diverge, using the words for different numbers, this can cause misunderstanding. Countries where the scale is currently used include most countries in continental Europe and most French-speaking, Spanish-speaking. The short scale is now used in most English-speaking and Arabic-speaking countries, in Brazil, in former Soviet Union, number names are rendered in the language of the country, but are similar everywhere due to shared etymology. Some languages, particularly in East Asia and South Asia, have large number naming systems that are different from both the long and short scales, for example the Indian numbering system. After several decades of increasing informal British usage of the scale, in 1974 the government of the UK adopted it. With very few exceptions, the British usage and American usage are now identical, the first recorded use of the terms short scale and long scale was by the French mathematician Geneviève Guitel in 1975. At and above a million the same names are used to refer to numbers differing by a factor of an integer power of 1,000. Each scale has a justification to explain the use of each such differing numerical name. The short-scale logic is based on powers of one thousand, whereas the long-scale logic is based on powers of one million, in both scales, the prefix bi- refers to 2 and tri- refers to 3, etc. However only in the scale do the prefixes beyond one million indicate the actual power or exponent. In the short scale, the prefixes refer to one less than the exponent, the word, million, derives from the Old French, milion, from the earlier Old Italian, milione, an intensification of the Latin word, mille, a thousand. That is, a million is a big thousand, much as a great gross is a dozen gross or 12×144 =1728, the word, milliard, or its translation, is found in many European languages and is used in those languages for 109. However, it is unknown in American English, which uses billion, and not used in British English, which preferred to use thousand million before the current usage of billion. The financial term, yard, which derives from milliard, is used on financial markets, as, unlike the term, billion, it is internationally unambiguous and phonetically distinct from million. Likewise, many long scale use the word billiard for one thousand long scale billions
12.
Orders of magnitude (numbers)
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This list contains selected positive numbers in increasing order, including counts of things, dimensionless quantity and probabilities. Mathematics – Writing, Approximately 10−183,800 is a rough first estimate of the probability that a monkey, however, taking punctuation, capitalization, and spacing into account, the actual probability is far lower, around 10−360,783. Computing, The number 1×10−6176 is equal to the smallest positive non-zero value that can be represented by a quadruple-precision IEEE decimal floating-point value, Computing, The number 6. 5×10−4966 is approximately equal to the smallest positive non-zero value that can be represented by a quadruple-precision IEEE floating-point value. Computing, The number 3. 6×10−4951 is approximately equal to the smallest positive non-zero value that can be represented by a 80-bit x86 double-extended IEEE floating-point value. Computing, The number 1×10−398 is equal to the smallest positive non-zero value that can be represented by a double-precision IEEE decimal floating-point value, Computing, The number 4. 9×10−324 is approximately equal to the smallest positive non-zero value that can be represented by a double-precision IEEE floating-point value. Computing, The number 1×10−101 is equal to the smallest positive non-zero value that can be represented by a single-precision IEEE decimal floating-point value, Mathematics, The probability in a game of bridge of all four players getting a complete suit is approximately 4. 47×10−28. ISO, yocto- ISO, zepto- Mathematics, The probability of matching 20 numbers for 20 in a game of keno is approximately 2.83 × 10−19. ISO, atto- Mathematics, The probability of rolling snake eyes 10 times in a row on a pair of dice is about 2. 74×10−16. ISO, micro- Mathematics – Poker, The odds of being dealt a flush in poker are 649,739 to 1 against. Mathematics – Poker, The odds of being dealt a flush in poker are 72,192 to 1 against. Mathematics – Poker, The odds of being dealt a four of a kind in poker are 4,164 to 1 against, for a probability of 2.4 × 10−4. ISO, milli- Mathematics – Poker, The odds of being dealt a full house in poker are 693 to 1 against, for a probability of 1.4 × 10−3. Mathematics – Poker, The odds of being dealt a flush in poker are 507.8 to 1 against, Mathematics – Poker, The odds of being dealt a straight in poker are 253.8 to 1 against, for a probability of 4 × 10−3. Physics, α =0.007297352570, the fine-structure constant, ISO, deci- Mathematics – Poker, The odds of being dealt only one pair in poker are about 5 to 2 against, for a probability of 0.42. Demography, The population of Monowi, a village in Nebraska. Mathematics, √2 ≈1.414213562373095489, the ratio of the diagonal of a square to its side length. Mathematics, φ ≈1.618033988749895848, the golden ratio Mathematics, the number system understood by most computers, human scale, There are 10 digits on a pair of human hands, and 10 toes on a pair of human feet. Mathematics, The number system used in life, the decimal system, has 10 digits,0,1,2,3,4,5,6,7,8,9
13.
1000000000 (number)
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1,000,000,000 is the natural number following 999,999,999 and preceding 1,000,000,001. One billion can also be written as b or bn, in scientific notation, it is written as 1 ×109. The SI prefix giga indicates 1,000,000,000 times the base unit, one billion years may be called eon in astronomy and geology. Previously in British English, the word billion referred exclusively to a million millions, however, this is no longer as common as earlier, and the word has been used to mean one thousand million for some time. The alternative term one thousand million is used in the U. K. or countries such as Spain that uses one thousand million as one million million constitutes a billion. The worded figure, as opposed to the figure is used to differentiate between one thousand million or one billion. The term milliard can also be used to refer to 1,000,000,000, whereas milliard is seldom used in English, in the South Asian numbering system, it is known as 100 crore or 1 Arab. 1000000007 – smallest prime number with 10 digits,1023456789 – smallest pandigital number in base 10. 1026753849 – smallest pandigital square that includes 0,1073741824 –2301073807359 – 14th Kynea number. 1162261467 –3191220703125 –513 1232922769- 35113^2 Centered hexagonal number,1234567890 – pandigital number with the digits in order. 1882341361 – The least prime whose reversal is both square and triangular,1977326743 –7112147483647 – 8th Mersenne prime and the largest signed 32-bit integer. 2147483648 –2312176782336 –6122214502422 – 6th primary pseudoperfect number,2357947691 –1192971215073 – 11th Fibonacci prime. 3405691582 – hexadecimal CAFEBABE, used as a placeholder in programming,3405697037 – hexadecimal CAFED00D, used as a placeholder in programming. 3735928559 – hexadecimal DEADBEEF, used as a placeholder in programming,3486784401 –3204294836223 – 16th Carol number. 4294967291 – Largest prime 32-bit unsigned integer,4294967295 – Maximum 32-bit unsigned integer, perfect totient number, product of the five prime Fermat numbers. 4294967296 –2324294967297 – the first composite Fermat number,6103515625 –5146210001000 – only self-descriptive number in base 10. 6975757441 –1786983776800 – 15th colossally abundant number, 15th superior highly composite number 7645370045 – 27th Pell number,8589934592 –2339043402501 – 25th Motzkin number. 9814072356 – largest square pandigital number, largest pandigital pure power,9876543210 – largest number without redundant digits
14.
1000000 (number)
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One million or one thousand thousand is the natural number following 999,999 and preceding 1,000,001. The word is derived from the early Italian millione, from mille, thousand and it is commonly abbreviated as m or M, further MM, mm, or mn in financial contexts. In scientific notation, it is written as 1×106 or 106, physical quantities can also be expressed using the SI prefix mega, when dealing with SI units, for example,1 megawatt equals 1,000,000 watts. The meaning of the word million is common to the scale and long scale numbering systems, unlike the larger numbers. Information, Not counting spaces, the text printed on 136 pages of an Encyclopædia Britannica, length, There are one million millimeters in a kilometer, and roughly a million sixteenths of an inch in a mile. A typical car tire might rotate a million times in a 1, 200-mile trip, fingers, If the width of a human finger is 2.2 cm, then a million fingers lined up would cover a distance of 22 km. If a person walks at a speed of 4 km/h, it would take approximately five. A city lot 70 by 100 feet is about a million square inches, volume, The cube root of one million is only one hundred, so a million objects or cubic units is contained in a cube only a hundred objects or linear units on a side. A million grains of salt or granulated sugar occupies only about 64 ml. One million cubic inches would be the volume of a room only 8 1⁄3 feet long by 8 1⁄3 feet wide by 8 1⁄3 feet high. Mass, A million cubic millimeters of water would have a volume of one litre, a million millilitres or cubic centimetres of water has a mass of a million grams or one tonne. Weight, A million 80-milligram honey bees would weigh the same as an 80 kg person, landscape, A pyramidal hill 600 feet wide at the base and 100 feet high would weigh about a million tons. Computer, A display resolution of 1,280 by 800 pixels contains 1,024,000 pixels, money, A USD bill of any denomination weighs 1 gram. There are 454 grams in a pound, one million $1 bills would weigh 2,204.62 pounds, or just over 1 ton. Time, A million seconds is 11.57 days, in Indian English and Pakistani English, it is also expressed as 10 lakh or 10 Lac. Lakh is derived from laksh for 100,000 in Sanskrit
15.
100 (number)
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100 or one hundred is the natural number following 99 and preceding 101. In medieval contexts, it may be described as the hundred or five score in order to differentiate the English. The standard SI prefix for a hundred is hecto-,100 is the basis of percentages, with 100% being a full amount. 100 is the sum of the first nine prime numbers, as well as the sum of pairs of prime numbers e. g.3 +97,11 +89,17 +83,29 +71,41 +59. 100 is the sum of the cubes of the first four integers and this is related by Nicomachuss theorem to the fact that 100 also equals the square of the sum of the first four integers,100 =102 =2. 26 +62 =100, thus 100 is a Leyland number and it is divisible by the number of primes below it,25 in this case. It can not be expressed as the difference between any integer and the total of coprimes below it, making it a noncototient and it can be expressed as a sum of some of its divisors, making it a semiperfect number. 100 is a Harshad number in base 10, and also in base 4, there are exactly 100 prime numbers whose digits are in strictly ascending order. 100 is the smallest number whose common logarithm is a prime number,100 senators are in the U. S One hundred is the atomic number of fermium, an actinide. On the Celsius scale,100 degrees is the temperature of pure water at sea level. The Kármán line lies at an altitude of 100 kilometres above the Earths sea level and is used to define the boundary between Earths atmosphere and outer space. There are 100 blasts of the Shofar heard in the service of Rosh Hashana, a religious Jew is expected to utter at least 100 blessings daily. In Hindu Religion - Mythology Book Mahabharata - Dhritarashtra had 100 sons known as kauravas, the United States Senate has 100 Senators. Most of the currencies are divided into 100 subunits, for example, one euro is one hundred cents. The 100 Euro banknotes feature a picture of a Rococo gateway on the obverse, the U. S. hundred-dollar bill has Benjamin Franklins portrait, the Benjamin is the largest U. S. bill in print. American savings bonds of $100 have Thomas Jeffersons portrait, while American $100 treasury bonds have Andrew Jacksons portrait, One hundred is also, The number of years in a century. The number of pounds in an American short hundredweight, in Greece, India, Israel and Nepal,100 is the police telephone number. In Belgium,100 is the ambulance and firefighter telephone number, in United Kingdom,100 is the operator telephone number
16.
10 (number)
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10 is an even natural number following 9 and preceding 11. Ten is the base of the numeral system, by far the most common system of denoting numbers in both spoken and written language. The reason for the choice of ten is assumed to be that humans have ten fingers, a collection of ten items is called a decade. The ordinal adjective is decimal, the adjective is denary. Increasing a quantity by one order of magnitude is most widely understood to mean multiplying the quantity by ten, to reduce something by one tenth is to decimate. A theoretical highest number in topics that require a rating, by contrast having 0 or 1 as the lowest number, Ten is a composite number, its proper divisors being 1,2 and 5. Ten is the smallest noncototient, a number that cannot be expressed as the difference between any integer and the number of coprimes below it. Ten is the discrete semiprime and the second member of the discrete semiprime family. Ten has an aliquot sum σ of 8 and is accordingly the first discrete semiprime to be in deficit, all subsequent discrete semiprimes are in deficit. The aliquot sequence for 10 comprises five members with this number being the second member of the 7-aliquot tree. Ten is the smallest semiprime that is the sum of all the prime numbers from its lower factor through its higher factor Only three other small semiprimes share this attribute. It is the sum of only one number the discrete semiprime 14. Ten is the sum of the first three numbers, of the four first numbers, of the square of the two first odd numbers and also of the first four factorials. Ten is the eighth Perrin number, preceded in the sequence by 5,5,7, a polygon with ten sides is a decagon, and 10 is a decagonal number. Because 10 is the product of a power of 2 with nothing but distinct Fermat primes, Ten is also a triangular number, a centered triangular number, and a tetrahedral number. Ten is the number of n queens problem solutions for n =5, Ten is the smallest number whose status as a possible friendly number is unknown. As is the case for any base in its system, ten is the first two-digit number in decimal, any integer written in the decimal system can be multiplied by ten by adding a zero to the end. The Roman numeral for ten is X, it is thought that the V for five is derived from an open hand, incidentally, the Chinese word numeral for ten, is also a cross, 十
17.
1 (number)
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1, is a number, a numeral, and the name of the glyph representing that number. It represents a single entity, the unit of counting or measurement, for example, a line segment of unit length is a line segment of length 1. It is also the first of the series of natural numbers. The word one can be used as a noun, an adjective and it comes from the English word an, which comes from the Proto-Germanic root *ainaz. The Proto-Germanic root *ainaz comes from the Proto-Indo-European root *oi-no-, compare the Proto-Germanic root *ainaz to Old Frisian an, Gothic ains, Danish een, Dutch een, German eins and Old Norse einn. Compare the Proto-Indo-European root *oi-no- to Greek oinos, Latin unus, Old Persian aivam, Old Church Slavonic -inu and ino-, Lithuanian vienas, Old Irish oin, One, sometimes referred to as unity, is the first non-zero natural number. It is thus the integer before two and after zero, and the first positive odd number, any number multiplied by one is that number, as one is the identity for multiplication. As a result,1 is its own factorial, its own square, its own cube, One is also the result of the empty product, as any number multiplied by one is itself. It is also the natural number that is neither composite nor prime with respect to division. The Gupta wrote it as a line, and the Nagari sometimes added a small circle on the left. The Nepali also rotated it to the right but kept the circle small and this eventually became the top serif in the modern numeral, but the occasional short horizontal line at the bottom probably originates from similarity with the Roman numeral I. Where the 1 is written with an upstroke, the number 7 has a horizontal stroke through the vertical line. While the shape of the 1 character has an ascender in most modern typefaces, in typefaces with text figures, many older typewriters do not have a separate symbol for 1 and use the lowercase letter l instead. It is possible to find cases when the uppercase J is used,1 cannot be used as the base of a positional numeral system, as the only digit that would be permitted in such a system would be 0. Since the base 1 exponential function always equals 1, its inverse does not exist, there are two ways to write the real number 1 as a recurring decimal, as 1.000. and as 0.999. There is only one way to represent the real number 1 as a Dedekind cut, in a multiplicative group or monoid, the identity element is sometimes denoted 1, but e is also traditional. However,1 is especially common for the identity of a ring. When such a ring has characteristic n not equal to 0,1 is the first figurate number of every kind, such as triangular number, pentagonal number and centered hexagonal number, to name just a few
18.
Mass
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In physics, mass is a property of a physical body. It is the measure of a resistance to acceleration when a net force is applied. It also determines the strength of its gravitational attraction to other bodies. The basic SI unit of mass is the kilogram, Mass is not the same as weight, even though mass is often determined by measuring the objects weight using a spring scale, rather than comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity and this is because weight is a force, while mass is the property that determines the strength of this force. In Newtonian physics, mass can be generalized as the amount of matter in an object, however, at very high speeds, special relativity postulates that energy is an additional source of mass. Thus, any body having mass has an equivalent amount of energy. In addition, matter is a defined term in science. There are several distinct phenomena which can be used to measure mass, active gravitational mass measures the gravitational force exerted by an object. Passive gravitational mass measures the force exerted on an object in a known gravitational field. The mass of an object determines its acceleration in the presence of an applied force, according to Newtons second law of motion, if a body of fixed mass m is subjected to a single force F, its acceleration a is given by F/m. A bodys mass also determines the degree to which it generates or is affected by a gravitational field and this is sometimes referred to as gravitational mass. The standard International System of Units unit of mass is the kilogram, the kilogram is 1000 grams, first defined in 1795 as one cubic decimeter of water at the melting point of ice. Then in 1889, the kilogram was redefined as the mass of the prototype kilogram. As of January 2013, there are proposals for redefining the kilogram yet again. In this context, the mass has units of eV/c2, the electronvolt and its multiples, such as the MeV, are commonly used in particle physics. The atomic mass unit is 1/12 of the mass of a carbon-12 atom, the atomic mass unit is convenient for expressing the masses of atoms and molecules. Outside the SI system, other units of mass include, the slug is an Imperial unit of mass, the pound is a unit of both mass and force, used mainly in the United States
19.
SI base unit
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The International System of Units defines seven units of measure as a basic set from which all other SI units can be derived. The SI base units form a set of mutually independent dimensions as required by dimensional analysis commonly employed in science, thus, the kelvin, named after Lord Kelvin, has the symbol K and the ampere, named after André-Marie Ampère, has the symbol A. Many other units, such as the litre, are not part of the SI. The definitions of the units have been modified several times since the Metre Convention in 1875. Since the redefinition of the metre in 1960, the kilogram is the unit that is directly defined in terms of a physical artifact. However, the mole, the ampere, and the candela are linked through their definitions to the mass of the platinum–iridium cylinder stored in a vault near Paris. It has long been an objective in metrology to define the kilogram in terms of a fundamental constant, two possibilities have attracted particular attention, the Planck constant and the Avogadro constant. The 23rd CGPM decided to postpone any formal change until the next General Conference in 2011
20.
Exponentiation
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Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent n. The exponent is usually shown as a superscript to the right of the base, Some common exponents have their own names, the exponent 2 is called the square of b or b squared, the exponent 3 is called the cube of b or b cubed. The exponent −1 of b, or 1 / b, is called the reciprocal of b, when n is a positive integer and b is not zero, b−n is naturally defined as 1/bn, preserving the property bn × bm = bn + m. The definition of exponentiation can be extended to any real or complex exponent. Exponentiation by integer exponents can also be defined for a variety of algebraic structures. The term power was used by the Greek mathematician Euclid for the square of a line, archimedes discovered and proved the law of exponents, 10a 10b = 10a+b, necessary to manipulate powers of 10. In the late 16th century, Jost Bürgi used Roman numerals for exponents, early in the 17th century, the first form of our modern exponential notation was introduced by Rene Descartes in his text titled La Géométrie, there, the notation is introduced in Book I. Nicolas Chuquet used a form of notation in the 15th century. The word exponent was coined in 1544 by Michael Stifel, samuel Jeake introduced the term indices in 1696. In the 16th century Robert Recorde used the square, cube, zenzizenzic, sursolid, zenzicube, second sursolid. Biquadrate has been used to refer to the power as well. Some mathematicians used exponents only for greater than two, preferring to represent squares as repeated multiplication. Thus they would write polynomials, for example, as ax + bxx + cx3 + d, another historical synonym, involution, is now rare and should not be confused with its more common meaning. In 1748 Leonhard Euler wrote consider exponentials or powers in which the exponent itself is a variable and it is clear that quantities of this kind are not algebraic functions, since in those the exponents must be constant. With this introduction of transcendental functions, Euler laid the foundation for the introduction of natural logarithm as the inverse function for y = ex. The expression b2 = b ⋅ b is called the square of b because the area of a square with side-length b is b2, the expression b3 = b ⋅ b ⋅ b is called the cube of b because the volume of a cube with side-length b is b3. The exponent indicates how many copies of the base are multiplied together, for example,35 =3 ⋅3 ⋅3 ⋅3 ⋅3 =243. The base 3 appears 5 times in the multiplication, because the exponent is 5
21.
Square kilometre
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Square kilometre or square kilometer, symbol km2, is a multiple of the square metre, the SI unit of area or surface area. For example,3 km2 is equal to 3×2 =3,000,000 m2, topographical map grids are worked out in metres, with the grid lines being 1,000 metres apart. 1,100,000 maps are divided into squares representing 1 km2, each square on the map being one square centimetre in area, for 1,50,000 maps, the grid lines are 2 cm apart. Each square on the map is 2 cm by 2 cm, for 1,25,000 maps, the grid lines are 4 cm apart. Each square on the map is 4 cm by 4 cm, in each case, the grid lines enclose one square kilometre. The area enclosed by the walls of many European medieval cities were about one square kilometre, the approximate area of the old walled cities can often be worked out by fitting the course of the wall to a rectangle or an oval. Examples include Delft, Netherlands 52°0′54″N 4°21′34″E The walled city of Delft was approximately rectangular, the approximate length of rectangle was about 1.30 kilometres. The approximate width of the rectangle was about 0.75 kilometres, a perfect rectangle with these measurements has an area of 1. 30×0.75 =0.9 km2 Lucca 43°50′38″N 10°30′2″E The medieval city is roughly rectangular with rounded north-east and north-west corners. The maximum distance from east to west is 1.36 kilometres, the maximum distance from north to south is 0.80 kilometres. A perfect rectangle of these dimensions would be 1. 36×0.80 =1.088 km2, Brugge 51°12′39″N 3°13′28″E The medieval city of Brugge, a major centre in Flanders, was roughly oval or elliptical in shape with the longer or semi-major axis running north and south. The maximum distance from north to south is 2.53 kilometres, the maximum distance from east to west is 1.81 kilometres. A perfect ellipse of these dimensions would be 2.53 ×1.81 × =3.597 km2. Chester United Kingdom 53°12′1″N 2°52′45″W Chester is one of the smaller English cities that has a city wall. The distance from Northgate to Watergate is about 855 metres. The distance from Eastgate to Westgate is about 589 metres, a perfect rectangle of these dimensions would be × =0.504 km2. Parks come in all sizes, a few are almost exactly one kilometre in area. Here are some examples, Riverside Country Park, UK. Brierley Forest Park, rio de Los Angeles State Park, California, USA Jones County Central Park, Iowa, USA. Using the figures published by golf course architects Crafter and Mogford, assuming a 6,000 metres 18-hole course, an area of 80 hectares needs to be allocated for the course itself
22.
Area
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Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane. Surface area is its analog on the surface of a three-dimensional object. It is the analog of the length of a curve or the volume of a solid. The area of a shape can be measured by comparing the shape to squares of a fixed size, in the International System of Units, the standard unit of area is the square metre, which is the area of a square whose sides are one metre long. A shape with an area of three square metres would have the area as three such squares. In mathematics, the square is defined to have area one. There are several formulas for the areas of simple shapes such as triangles, rectangles. Using these formulas, the area of any polygon can be found by dividing the polygon into triangles, for shapes with curved boundary, calculus is usually required to compute the area. Indeed, the problem of determining the area of plane figures was a motivation for the historical development of calculus. For a solid such as a sphere, cone, or cylinder. Formulas for the areas of simple shapes were computed by the ancient Greeks. Area plays an important role in modern mathematics, in addition to its obvious importance in geometry and calculus, area is related to the definition of determinants in linear algebra, and is a basic property of surfaces in differential geometry. In analysis, the area of a subset of the plane is defined using Lebesgue measure, in general, area in higher mathematics is seen as a special case of volume for two-dimensional regions. Area can be defined through the use of axioms, defining it as a function of a collection of certain plane figures to the set of real numbers and it can be proved that such a function exists. An approach to defining what is meant by area is through axioms, area can be defined as a function from a collection M of special kind of plane figures to the set of real numbers which satisfies the following properties, For all S in M, a ≥0. If S and T are in M then so are S ∪ T and S ∩ T, if S and T are in M with S ⊆ T then T − S is in M and a = a − a. If a set S is in M and S is congruent to T then T is also in M, every rectangle R is in M. If the rectangle has length h and breadth k then a = hk, let Q be a set enclosed between two step regions S and T
23.
Square (geometry)
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In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle in which two adjacent sides have equal length, a square with vertices ABCD would be denoted ◻ ABCD. e. A rhombus with equal diagonals a convex quadrilateral with sides a, b, c, d whose area is A =12 =12. Opposite sides of a square are both parallel and equal in length, all four angles of a square are equal. All four sides of a square are equal, the diagonals of a square are equal. The square is the n=2 case of the families of n-hypercubes and n-orthoplexes, a truncated square, t, is an octagon. An alternated square, h, is a digon, the perimeter of a square whose four sides have length ℓ is P =4 ℓ and the area A is A = ℓ2. In classical times, the power was described in terms of the area of a square. This led to the use of the square to mean raising to the second power. The area can also be calculated using the diagonal d according to A = d 22. In terms of the circumradius R, the area of a square is A =2 R2, since the area of the circle is π R2, in terms of the inradius r, the area of the square is A =4 r 2. Because it is a polygon, a square is the quadrilateral of least perimeter enclosing a given area. Dually, a square is the quadrilateral containing the largest area within a given perimeter. Indeed, if A and P are the area and perimeter enclosed by a quadrilateral, then the isoperimetric inequality holds,16 A ≤ P2 with equality if. The diagonals of a square are 2 times the length of a side of the square and this value, known as the square root of 2 or Pythagoras constant, was the first number proven to be irrational. A square can also be defined as a parallelogram with equal diagonals that bisect the angles, if a figure is both a rectangle and a rhombus, then it is a square. If a circle is circumscribed around a square, the area of the circle is π /2 times the area of the square, if a circle is inscribed in the square, the area of the circle is π /4 times the area of the square. A square has an area than any other quadrilateral with the same perimeter
24.
Megametre
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The megametre or megameter is a unit of length in the metric system, equal to one million metres, the SI base unit of length, hence to 1000 km or approximately 621.37 miles. Megametres are rarely seen in use, e. g.5000 km is much more common than 5 Mm. The symbol can also be confused with millimetres, megametres are also occasionally found in science fiction. The Earths polar circumference is 39.94 Mm, the distance from Amsterdam to Marseille is 1.01 Mm. The distance from New York City to Chicago is 1.14 Mm, the Earths equatorial diameter is 12.76 Mm. Quebec provinces total area is 1.542 Mm2, the mean distance from the Earth to the Moon is 384.4 Mm. Jupiters equatorial diameter is 143 Mm, the speed of light is exactly 299.792458 Mm/s by the definition of the metre. SI SI prefix Metric system Orders of magnitude Conversion of units, for comparison with other units of length Light year Parsec
25.
Volume
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Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance or shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic metre, three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, such as regular, straight-edged, volumes of a complicated shape can be calculated by integral calculus if a formula exists for the shapes boundary. Where a variance in shape and volume occurs, such as those that exist between different human beings, these can be calculated using techniques such as the Body Volume Index. One-dimensional figures and two-dimensional shapes are assigned zero volume in the three-dimensional space, the volume of a solid can be determined by fluid displacement. Displacement of liquid can also be used to determine the volume of a gas, the combined volume of two substances is usually greater than the volume of one of the substances. However, sometimes one substance dissolves in the other and the volume is not additive. In differential geometry, volume is expressed by means of the volume form, in thermodynamics, volume is a fundamental parameter, and is a conjugate variable to pressure. Any unit of length gives a unit of volume, the volume of a cube whose sides have the given length. For example, a cubic centimetre is the volume of a cube whose sides are one centimetre in length, in the International System of Units, the standard unit of volume is the cubic metre. The metric system also includes the litre as a unit of volume, thus 1 litre =3 =1000 cubic centimetres =0.001 cubic metres, so 1 cubic metre =1000 litres. Small amounts of liquid are often measured in millilitres, where 1 millilitre =0.001 litres =1 cubic centimetre. Capacity is defined by the Oxford English Dictionary as the applied to the content of a vessel, and to liquids, grain, or the like. Capacity is not identical in meaning to volume, though closely related, Units of capacity are the SI litre and its derived units, and Imperial units such as gill, pint, gallon, and others. Units of volume are the cubes of units of length, in SI the units of volume and capacity are closely related, one litre is exactly 1 cubic decimetre, the capacity of a cube with a 10 cm side. In other systems the conversion is not trivial, the capacity of a fuel tank is rarely stated in cubic feet, for example. The density of an object is defined as the ratio of the mass to the volume, the inverse of density is specific volume which is defined as volume divided by mass. Specific volume is an important in thermodynamics where the volume of a working fluid is often an important parameter of a system being studied
26.
Cube
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Beryllium copper, also known as copper beryllium, beryllium bronze and spring copper, is a copper alloy with 0. 5—3% beryllium and sometimes other elements. Beryllium copper combines high strength with non-magnetic and non-sparking qualities and it has excellent metalworking, forming and machining properties. It has many specialized applications in tools for hazardous environments, musical instruments, precision measurement devices, bullets, beryllium alloys present a toxic inhalation hazard during manufacture. Beryllium copper is a ductile, weldable, and machinable alloy and it is resistant to non-oxidizing acids, to plastic decomposition products, to abrasive wear, and to galling. It can be heat-treated for increased strength, durability, and electrical conductivity, beryllium copper attains the greatest strength of any copper-based alloy. In solid form and as finished objects, beryllium copper presents no known health hazard, however, inhalation of dust, mist, or fume containing beryllium can cause the serious lung condition, chronic beryllium disease. That disease affects primarily the lungs, restricting the exchange of oxygen between the lungs and the bloodstream, the International Agency for Research on Cancer lists beryllium as a Group 1 Human Carcinogen. The National Toxicology Program also lists beryllium as a carcinogen, beryllium copper is a non-ferrous alloy used in springs, spring wire, load cells, and other parts that must retain their shape under repeated stress and strain. It has high electrical conductivity, and is used in low-current contacts for batteries, beryllium copper is non-sparking but physically tough and nonmagnetic, fulfilling the requirements of ATEX directive for Zones 0,1, and 2. Beryllium copper screwdrivers, pliers, wrenches, cold chisels, knives, and hammers are available for environments with explosive hazards, such oil rigs, coal mines, an alternative metal sometimes used for non-sparking tools is aluminium bronze. Compared to steel tools, beryllium copper tools are more expensive, not as strong, and less durable, beryllium copper is frequently used for percussion instruments for its consistent tone and resonance, especially tambourines and triangles. Beryllium copper has been used for armour piercing bullets, though usage is unusual because bullets made from steel alloys are much less expensive and have similar properties. Beryllium copper is used for measurement-while-drilling tools in the drilling industry. A non-magnetic alloy is required, as magnetometers are used for field-strength data received from the tool, beryllium copper gaskets are used to create an RF-tight, electronic seal on doors used with EMC testing and anechoic chambers. For a time, beryllium copper was used in the manufacture of clubs, particularly wedges. Though some golfers prefer the feel of BeCu club heads, regulatory issues, kiefer Plating of Elkhart, Indiana built some beryllium-copper trumpet bells for the Schilke Music Co. of Chicago. These light-weight bells produce a sound preferred by some musicians, beryllium copper wire is produced in many forms, round, square, flat and shaped, in coils, on spools and in straight lengths. Beryllium copper valve seats and guides are used in high performance engines with coated titanium valves
27.
Cubic metre
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The cubic metre or cubic meter is the SI derived unit of volume. It is the volume of a cube with one metre in length. An alternative name, which allowed a different usage with metric prefixes, was the stère, another alternative name, no longer widely used, was the kilolitre. A cubic metre of water at the temperature of maximum density and standard atmospheric pressure has a mass of 1000 kg. At 0 °C, the point of water, a cubic metre of water has slightly less mass,999.972 kilograms. It is sometimes abbreviated to cu m, m3, M3, m^3, m**3, CBM, abbreviated CBM and cbm in the freight business and MTQ in international trade. See Orders of magnitude for a comparison with other volumes
28.
Kilogram
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The kilogram or kilogramme is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype of the Kilogram. The avoirdupois pound, used in both the imperial and US customary systems, is defined as exactly 0.45359237 kg, making one kilogram approximately equal to 2.2046 avoirdupois pounds. Other traditional units of weight and mass around the world are also defined in terms of the kilogram, the gram, 1/1000 of a kilogram, was provisionally defined in 1795 as the mass of one cubic centimeter of water at the melting point of ice. The final kilogram, manufactured as a prototype in 1799 and from which the IPK was derived in 1875, had an equal to the mass of 1 dm3 of water at its maximum density. The kilogram is the only SI base unit with an SI prefix as part of its name and it is also the only SI unit that is still directly defined by an artifact rather than a fundamental physical property that can be reproduced in different laboratories. Three other base units and 17 derived units in the SI system are defined relative to the kilogram, only 8 other units do not require the kilogram in their definition, temperature, time and frequency, length, and angle. At its 2011 meeting, the CGPM agreed in principle that the kilogram should be redefined in terms of the Planck constant, the decision was originally deferred until 2014, in 2014 it was deferred again until the next meeting. There are currently several different proposals for the redefinition, these are described in the Proposed Future Definitions section below, the International Prototype Kilogram is rarely used or handled. In the decree of 1795, the term gramme thus replaced gravet, the French spelling was adopted in the United Kingdom when the word was used for the first time in English in 1797, with the spelling kilogram being adopted in the United States. In the United Kingdom both spellings are used, with kilogram having become by far the more common, UK law regulating the units to be used when trading by weight or measure does not prevent the use of either spelling. In the 19th century the French word kilo, a shortening of kilogramme, was imported into the English language where it has used to mean both kilogram and kilometer. In 1935 this was adopted by the IEC as the Giorgi system, now known as MKS system. In 1948 the CGPM commissioned the CIPM to make recommendations for a practical system of units of measurement. This led to the launch of SI in 1960 and the subsequent publication of the SI Brochure, the kilogram is a unit of mass, a property which corresponds to the common perception of how heavy an object is. Mass is a property, that is, it is related to the tendency of an object at rest to remain at rest, or if in motion to remain in motion at a constant velocity. Accordingly, for astronauts in microgravity, no effort is required to hold objects off the cabin floor, they are weightless. However, since objects in microgravity still retain their mass and inertia, the ratio of the force of gravity on the two objects, measured by the scale, is equal to the ratio of their masses. On April 7,1795, the gram was decreed in France to be the weight of a volume of pure water equal to the cube of the hundredth part of the metre
29.
Gram
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The gram is a metric system unit of mass. Originally defined as the weight of a volume of pure water equal to the cube of the hundredth part of a metre. The only unit symbol for gram that is recognised by the International System of Units is g following the numeric value with a space, the SI does not support the use of abbreviations such as gr, gm or Gm. The word gramme was adopted by the French National Convention in its 1795 decree revising the system as replacing the gravet introduced in 1793. Its definition remained that of the weight of a centimetre of water. French gramme was taken from the Late Latin term gramma and this word, ultimately from Greek γράμμα letter had adopted a specialised meaning in Late Antiquity of one twenty-fourth part of an ounce, corresponding to about 1.14 grams. This use of the term is found in the carmen de ponderibus et mensuris composed around 400 AD, the gram was the fundamental unit of mass in the 19th-century centimetre–gram–second system of units. The gram is today the most widely used unit of measurement for non-liquid ingredients in cooking and grocery shopping worldwide. 1 gram =15.4323583529 grains 1 grain =0.06479891 grams 1 avoirdupois ounce =28.349523125 grams 1 troy ounce =31.1034768 grams 100 grams =3.527396195 ounces 1 gram =5 carats 1 gram =8. 1 gram is roughly equal to 1 small paper clip or pen cap, the Japanese 1 yen coin has a mass of one gram. Conversion of units Duella Gold gram Orders of magnitude Gram at Encyclopædia Britannica
30.
Milligram
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The kilogram or kilogramme is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype of the Kilogram. The avoirdupois pound, used in both the imperial and US customary systems, is defined as exactly 0.45359237 kg, making one kilogram approximately equal to 2.2046 avoirdupois pounds. Other traditional units of weight and mass around the world are also defined in terms of the kilogram, the gram, 1/1000 of a kilogram, was provisionally defined in 1795 as the mass of one cubic centimetre of water at the melting point of ice. The final kilogram, manufactured as a prototype in 1799 and from which the IPK was derived in 1875, had an equal to the mass of 1 dm3 of water at its maximum density. The kilogram is the only SI base unit with an SI prefix as part of its name and it is also the only SI unit that is still directly defined by an artifact rather than a fundamental physical property that can be reproduced in different laboratories. Three other base units and 17 derived units in the SI system are defined relative to the kilogram, only 8 other units do not require the kilogram in their definition, temperature, time and frequency, length, and angle. At its 2011 meeting, the CGPM agreed in principle that the kilogram should be redefined in terms of the Planck constant, the decision was originally deferred until 2014, in 2014 it was deferred again until the next meeting. There are currently several different proposals for the redefinition, these are described in the Proposed Future Definitions section below, the International Prototype Kilogram is rarely used or handled. In the decree of 1795, the term gramme thus replaced gravet, the French spelling was adopted in the United Kingdom when the word was used for the first time in English in 1797, with the spelling kilogram being adopted in the United States. In the United Kingdom both spellings are used, with kilogram having become by far the more common, UK law regulating the units to be used when trading by weight or measure does not prevent the use of either spelling. In the 19th century the French word kilo, a shortening of kilogramme, was imported into the English language where it has used to mean both kilogram and kilometre. In 1935 this was adopted by the IEC as the Giorgi system, now known as MKS system. In 1948 the CGPM commissioned the CIPM to make recommendations for a practical system of units of measurement. This led to the launch of SI in 1960 and the subsequent publication of the SI Brochure, the kilogram is a unit of mass, a property which corresponds to the common perception of how heavy an object is. Mass is a property, that is, it is related to the tendency of an object at rest to remain at rest, or if in motion to remain in motion at a constant velocity. Accordingly, for astronauts in microgravity, no effort is required to hold objects off the cabin floor, they are weightless. However, since objects in microgravity still retain their mass and inertia, the ratio of the force of gravity on the two objects, measured by the scale, is equal to the ratio of their masses. On April 7,1795, the gram was decreed in France to be the weight of a volume of pure water equal to the cube of the hundredth part of the metre
31.
Tonne
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The SI symbol for the tonne is t, adopted at the same time as the unit itself in 1879. Its use is also official, for the metric ton, within the United States, having been adopted by the US National Institute of Standards and it is a symbol, not an abbreviation, and should not be followed by a period. Informal and non-approved symbols or abbreviations include T, mT, MT, in French and all English-speaking countries that are predominantly metric, tonne is the correct spelling. Before metrication in the UK the unit used for most purposes was the Imperial ton of 2,240 pounds avoirdupois, equivalent to 1,016 kg, differing by just 1. 6% from the tonne. Ton and tonne are both derived from a Germanic word in use in the North Sea area since the Middle Ages to designate a large cask. A full tun, standing about a high, could easily weigh a tonne. An English tun of wine weighs roughly a tonne,954 kg if full of water, in the United States, the unit was originally referred to using the French words millier or tonneau, but these terms are now obsolete. The Imperial and US customary units comparable to the tonne are both spelled ton in English, though they differ in mass, one tonne is equivalent to, Metric/SI,1 megagram. Equal to 1000000 grams or 1000 kilograms, megagram, Mg, is the official SI unit. Mg is distinct from mg, milligram, pounds, Exactly 1000/0. 453 592 37 lb, or approximately 2204.622622 lb. US/Short tons, Exactly 1/0. 907 184 74 short tons, or approximately 1.102311311 ST. One short ton is exactly 0.90718474 t, imperial/Long tons, Exactly 1/1. 016 046 9088 long tons, or approximately 0.9842065276 LT. One long ton is exactly 1.0160469088 t, for multiples of the tonne, it is more usual to speak of thousands or millions of tonnes. Kilotonne, megatonne, and gigatonne are more used for the energy of nuclear explosions and other events. When used in context, there is little need to distinguish between metric and other tons, and the unit is spelt either as ton or tonne with the relevant prefix attached. *The equivalent units columns use the short scale large-number naming system used in most English-language countries. †Values in the equivalent short and long tons columns are rounded to five significant figures, ǂThough non-standard, the symbol kt is also sometimes used for knot, a unit of speed for sea-going vessels, and should not be confused with kilotonne. A metric ton unit can mean 10 kilograms within metal trading and it traditionally referred to a metric ton of ore containing 1% of metal. In the case of uranium, the acronym MTU is sometimes considered to be metric ton of uranium, in the petroleum industry the tonne of oil equivalent is a unit of energy, the amount of energy released by burning one tonne of crude oil, approximately 42 GJ
32.
TNT equivalent
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TNT equivalent is a convention for expressing energy, typically used to describe the energy released in an explosion. The ton of TNT is a unit of energy defined by convention to be 4.184 gigajoules. The convention intends to compare the destructiveness of an event with that of conventional explosives, the kiloton is a unit of energy equal to 4.184 terajoules. The megaton is a unit of equal to 4.184 petajoules. The kiloton and megaton of TNT have traditionally used to describe the energy output. The TNT equivalent appears in various nuclear weapon control treaties, and has used to characterize the energy released in such other highly destructive events as an asteroid impact. A gram of TNT releases 2673–6702 J upon explosion, the energy liberated by one gram of TNT was arbitrarily defined as a matter of convention to be 4184 J, which is exactly one kilocalorie. The measured, pure heat output of a gram of TNT is only 2724 J, alternative TNT equivalency can be calculated as a function of when in the detonation the value is measured and which property is being compared. A kiloton of TNT can be visualized as a cube of TNT8.46 metres on a side, the RE factor is the relative mass of TNT to which an explosive is equivalent, the greater the RE, the more powerful the explosive. This enables engineers to determine the proper masses of different explosives when applying blasting formulas developed specifically for TNT. For example, if a timber-cutting formula calls for a charge of 1 kg of TNT, then based on octanitrocubanes RE factor of 2.38, using PETN, engineers would need 1. 0/1.66 kg to obtain the same effects as 1 kg of TNT. With ANFO or ammonium nitrate, they would require 1. 0/0.74 kg or 1. 0/0.42 kg, *, TBX or EBX, in a small, confined space, may have over twice the power of destruction. The total power of aluminized mixtures strictly depends on the condition of explosions, guide for the Use of the International System of Units. National Institute of Standards and Technology, nuclear Weapons FAQ Part 1.3 Rhodes, Richard. The Making of the Atomic Bomb, cooper, Paul W. Explosives Engineering, New York, Wiley-VCH, ISBN 0-471-18636-8 HQ Department of the Army, Field Manual 5-25, Explosives and Demolitions, Washington, D. C. Pentagon Publishing, pp. 83–84, ISBN 0-9759009-5-1 Explosives - Compositions, Alexandria, VA, thermobaric Explosives, Advanced Energetic Materials,2004. THE NATIONAL ACADEMIES PRESS, nap. edu, retrieved September 2004
33.
Scientific notation
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Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. It is commonly used by scientists, mathematicians and engineers, in part because it can simplify certain arithmetic operations, on scientific calculators it is known as SCI display mode. In scientific notation all numbers are written in the form m × 10n, where the exponent n is an integer, however, the term mantissa may cause confusion because it is the name of the fractional part of the common logarithm. If the number is then a minus sign precedes m. In normalized notation, the exponent is chosen so that the value of the coefficient is at least one. Decimal floating point is an arithmetic system closely related to scientific notation. Any given integer can be written in the form m×10^n in many ways, in normalized scientific notation, the exponent n is chosen so that the absolute value of m remains at least one but less than ten. Thus 350 is written as 3. 5×102 and this form allows easy comparison of numbers, as the exponent n gives the numbers order of magnitude. In normalized notation, the exponent n is negative for a number with absolute value between 0 and 1, the 10 and exponent are often omitted when the exponent is 0. Normalized scientific form is the form of expression of large numbers in many fields, unless an unnormalized form. Normalized scientific notation is often called exponential notation—although the latter term is general and also applies when m is not restricted to the range 1 to 10. Engineering notation differs from normalized scientific notation in that the exponent n is restricted to multiples of 3, consequently, the absolute value of m is in the range 1 ≤ |m| <1000, rather than 1 ≤ |m| <10. Though similar in concept, engineering notation is rarely called scientific notation, engineering notation allows the numbers to explicitly match their corresponding SI prefixes, which facilitates reading and oral communication. A significant figure is a digit in a number that adds to its precision and this includes all nonzero numbers, zeroes between significant digits, and zeroes indicated to be significant. Leading and trailing zeroes are not significant because they exist only to show the scale of the number. Therefore,1,230,400 usually has five significant figures,1,2,3,0, and 4, when a number is converted into normalized scientific notation, it is scaled down to a number between 1 and 10. All of the significant digits remain, but the place holding zeroes are no longer required, thus 1,230,400 would become 1.2304 ×106. However, there is also the possibility that the number may be known to six or more significant figures, thus, an additional advantage of scientific notation is that the number of significant figures is clearer
34.
Exponent
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Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent n. The exponent is usually shown as a superscript to the right of the base, Some common exponents have their own names, the exponent 2 is called the square of b or b squared, the exponent 3 is called the cube of b or b cubed. The exponent −1 of b, or 1 / b, is called the reciprocal of b, when n is a positive integer and b is not zero, b−n is naturally defined as 1/bn, preserving the property bn × bm = bn + m. The definition of exponentiation can be extended to any real or complex exponent. Exponentiation by integer exponents can also be defined for a variety of algebraic structures. The term power was used by the Greek mathematician Euclid for the square of a line, archimedes discovered and proved the law of exponents, 10a 10b = 10a+b, necessary to manipulate powers of 10. In the late 16th century, Jost Bürgi used Roman numerals for exponents, early in the 17th century, the first form of our modern exponential notation was introduced by Rene Descartes in his text titled La Géométrie, there, the notation is introduced in Book I. Nicolas Chuquet used a form of notation in the 15th century. The word exponent was coined in 1544 by Michael Stifel, samuel Jeake introduced the term indices in 1696. In the 16th century Robert Recorde used the square, cube, zenzizenzic, sursolid, zenzicube, second sursolid. Biquadrate has been used to refer to the power as well. Some mathematicians used exponents only for greater than two, preferring to represent squares as repeated multiplication. Thus they would write polynomials, for example, as ax + bxx + cx3 + d, another historical synonym, involution, is now rare and should not be confused with its more common meaning. In 1748 Leonhard Euler wrote consider exponentials or powers in which the exponent itself is a variable and it is clear that quantities of this kind are not algebraic functions, since in those the exponents must be constant. With this introduction of transcendental functions, Euler laid the foundation for the introduction of natural logarithm as the inverse function for y = ex. The expression b2 = b ⋅ b is called the square of b because the area of a square with side-length b is b2, the expression b3 = b ⋅ b ⋅ b is called the cube of b because the volume of a cube with side-length b is b3. The exponent indicates how many copies of the base are multiplied together, for example,35 =3 ⋅3 ⋅3 ⋅3 ⋅3 =243. The base 3 appears 5 times in the multiplication, because the exponent is 5
35.
Chemistry
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Chemistry is a branch of physical science that studies the composition, structure, properties and change of matter. Chemistry is sometimes called the science because it bridges other natural sciences, including physics. For the differences between chemistry and physics see comparison of chemistry and physics, the history of chemistry can be traced to alchemy, which had been practiced for several millennia in various parts of the world. The word chemistry comes from alchemy, which referred to a set of practices that encompassed elements of chemistry, metallurgy, philosophy, astrology, astronomy, mysticism. An alchemist was called a chemist in popular speech, and later the suffix -ry was added to this to describe the art of the chemist as chemistry, the modern word alchemy in turn is derived from the Arabic word al-kīmīā. In origin, the term is borrowed from the Greek χημία or χημεία and this may have Egyptian origins since al-kīmīā is derived from the Greek χημία, which is in turn derived from the word Chemi or Kimi, which is the ancient name of Egypt in Egyptian. Alternately, al-kīmīā may derive from χημεία, meaning cast together, in retrospect, the definition of chemistry has changed over time, as new discoveries and theories add to the functionality of the science. The term chymistry, in the view of noted scientist Robert Boyle in 1661, in 1837, Jean-Baptiste Dumas considered the word chemistry to refer to the science concerned with the laws and effects of molecular forces. More recently, in 1998, Professor Raymond Chang broadened the definition of chemistry to mean the study of matter, early civilizations, such as the Egyptians Babylonians, Indians amassed practical knowledge concerning the arts of metallurgy, pottery and dyes, but didnt develop a systematic theory. Greek atomism dates back to 440 BC, arising in works by such as Democritus and Epicurus. In 50 BC, the Roman philosopher Lucretius expanded upon the theory in his book De rerum natura, unlike modern concepts of science, Greek atomism was purely philosophical in nature, with little concern for empirical observations and no concern for chemical experiments. Work, particularly the development of distillation, continued in the early Byzantine period with the most famous practitioner being the 4th century Greek-Egyptian Zosimos of Panopolis. He formulated Boyles law, rejected the four elements and proposed a mechanistic alternative of atoms. Before his work, though, many important discoveries had been made, the Scottish chemist Joseph Black and the Dutchman J. B. English scientist John Dalton proposed the theory of atoms, that all substances are composed of indivisible atoms of matter. Davy discovered nine new elements including the alkali metals by extracting them from their oxides with electric current, british William Prout first proposed ordering all the elements by their atomic weight as all atoms had a weight that was an exact multiple of the atomic weight of hydrogen. The inert gases, later called the noble gases were discovered by William Ramsay in collaboration with Lord Rayleigh at the end of the century, thereby filling in the basic structure of the table. Organic chemistry was developed by Justus von Liebig and others, following Friedrich Wöhlers synthesis of urea which proved that organisms were, in theory
36.
Astronomical unit
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The astronomical unit is a unit of length, roughly the distance from Earth to the Sun. However, that varies as Earth orbits the Sun, from a maximum to a minimum. Originally conceived as the average of Earths aphelion and perihelion, it is now defined as exactly 149597870700 metres, the astronomical unit is used primarily as a convenient yardstick for measuring distances within the Solar System or around other stars. However, it is also a component in the definition of another unit of astronomical length. A variety of symbols and abbreviations have been in use for the astronomical unit. In a 1976 resolution, the International Astronomical Union used the symbol A for the astronomical unit, in 2006, the International Bureau of Weights and Measures recommended ua as the symbol for the unit. In 2012, the IAU, noting that various symbols are presently in use for the astronomical unit, in the 2014 revision of the SI Brochure, the BIPM used the unit symbol au. In ISO 80000-3, the symbol of the unit is ua. Earths orbit around the Sun is an ellipse, the semi-major axis of this ellipse is defined to be half of the straight line segment that joins the aphelion and perihelion. The centre of the sun lies on this line segment. In addition, it mapped out exactly the largest straight-line distance that Earth traverses over the course of a year, knowing Earths shift and a stars shift enabled the stars distance to be calculated. But all measurements are subject to some degree of error or uncertainty, improvements in precision have always been a key to improving astronomical understanding. Improving measurements were continually checked and cross-checked by means of our understanding of the laws of celestial mechanics, the expected positions and distances of objects at an established time are calculated from these laws, and assembled into a collection of data called an ephemeris. NASAs Jet Propulsion Laboratory provides one of several ephemeris computation services, in 1976, in order to establish a yet more precise measure for the astronomical unit, the IAU formally adopted a new definition. Equivalently, by definition, one AU is the radius of an unperturbed circular Newtonian orbit about the sun of a particle having infinitesimal mass. As with all measurements, these rely on measuring the time taken for photons to be reflected from an object. However, for precision the calculations require adjustment for such as the motions of the probe. In addition, the measurement of the time itself must be translated to a scale that accounts for relativistic time dilation
37.
Parsec
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The parsec is a unit of length used to measure large distances to objects outside the Solar System. One parsec is the distance at which one astronomical unit subtends an angle of one arcsecond, a parsec is equal to about 3.26 light-years in length. The nearest star, Proxima Centauri, is about 1.3 parsecs from the Sun, most of the stars visible to the unaided eye in the nighttime sky are within 500 parsecs of the Sun. The parsec unit was likely first suggested in 1913 by the British astronomer Herbert Hall Turner, named from an abbreviation of the parallax of one arcsecond, it was defined so as to make calculations of astronomical distances quick and easy for astronomers from only their raw observational data. Partly for this reason, it is still the unit preferred in astronomy and astrophysics, though the light-year remains prominent in science texts. This corresponds to the definition of the parsec found in many contemporary astronomical references. Derivation, create a triangle with one leg being from the Earth to the Sun. As that point in space away, the angle between the Sun and Earth decreases. A parsec is the length of that leg when the angle between the Sun and Earth is one arc-second. One of the oldest methods used by astronomers to calculate the distance to a star is to record the difference in angle between two measurements of the position of the star in the sky. The first measurement is taken from the Earth on one side of the Sun, and the second is approximately half a year later. The distance between the two positions of the Earth when the two measurements were taken is twice the distance between the Earth and the Sun. The difference in angle between the two measurements is twice the angle, which is formed by lines from the Sun. Then the distance to the star could be calculated using trigonometry. 5-parsec distance of 61 Cygni, the parallax of a star is defined as half of the angular distance that a star appears to move relative to the celestial sphere as Earth orbits the Sun. Equivalently, it is the angle, from that stars perspective. The star, the Sun and the Earth form the corners of a right triangle in space, the right angle is the corner at the Sun. Therefore, given a measurement of the angle, along with the rules of trigonometry. A parsec is defined as the length of the adjacent to the vertex occupied by a star whose parallax angle is one arcsecond
38.
National Institute of Standards and Technology
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The National Institute of Standards and Technology is a measurement standards laboratory, and a non-regulatory agency of the United States Department of Commerce. Its mission is to promote innovation and industrial competitiveness, in 1821, John Quincy Adams had declared Weights and measures may be ranked among the necessities of life to every individual of human society. From 1830 until 1901, the role of overseeing weights and measures was carried out by the Office of Standard Weights and Measures, president Theodore Roosevelt appointed Samuel W. Stratton as the first director. The budget for the first year of operation was $40,000, a laboratory site was constructed in Washington, DC, and instruments were acquired from the national physical laboratories of Europe. In addition to weights and measures, the Bureau developed instruments for electrical units, in 1905 a meeting was called that would be the first National Conference on Weights and Measures. Quality standards were developed for products including some types of clothing, automobile brake systems and headlamps, antifreeze, during World War I, the Bureau worked on multiple problems related to war production, even operating its own facility to produce optical glass when European supplies were cut off. Between the wars, Harry Diamond of the Bureau developed a blind approach radio aircraft landing system, in 1948, financed by the Air Force, the Bureau began design and construction of SEAC, the Standards Eastern Automatic Computer. The computer went into operation in May 1950 using a combination of vacuum tubes, about the same time the Standards Western Automatic Computer, was built at the Los Angeles office of the NBS and used for research there. A mobile version, DYSEAC, was built for the Signal Corps in 1954, due to a changing mission, the National Bureau of Standards became the National Institute of Standards and Technology in 1988. Following 9/11, NIST conducted the investigation into the collapse of the World Trade Center buildings. NIST had a budget for fiscal year 2007 of about $843.3 million. NISTs 2009 budget was $992 million, and it also received $610 million as part of the American Recovery, NIST employs about 2,900 scientists, engineers, technicians, and support and administrative personnel. About 1,800 NIST associates complement the staff, in addition, NIST partners with 1,400 manufacturing specialists and staff at nearly 350 affiliated centers around the country. NIST publishes the Handbook 44 that provides the Specifications, tolerances, the Congress of 1866 made use of the metric system in commerce a legally protected activity through the passage of Metric Act of 1866. NIST is headquartered in Gaithersburg, Maryland, and operates a facility in Boulder, nISTs activities are organized into laboratory programs and extramural programs. Effective October 1,2010, NIST was realigned by reducing the number of NIST laboratory units from ten to six, nISTs Boulder laboratories are best known for NIST‑F1, which houses an atomic clock. NIST‑F1 serves as the source of the official time. NIST also operates a neutron science user facility, the NIST Center for Neutron Research, the NCNR provides scientists access to a variety of neutron scattering instruments, which they use in many research fields
39.
Radian
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The radian is the standard unit of angular measure, used in many areas of mathematics. The length of an arc of a circle is numerically equal to the measurement in radians of the angle that it subtends. The unit was formerly an SI supplementary unit, but this category was abolished in 1995, separately, the SI unit of solid angle measurement is the steradian. The radian is represented by the symbol rad, so for example, a value of 1.2 radians could be written as 1.2 rad,1.2 r,1. 2rad, or 1. 2c. Radian describes the angle subtended by a circular arc as the length of the arc divided by the radius of the arc. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. Conversely, the length of the arc is equal to the radius multiplied by the magnitude of the angle in radians. As the ratio of two lengths, the radian is a number that needs no unit symbol, and in mathematical writing the symbol rad is almost always omitted. When quantifying an angle in the absence of any symbol, radians are assumed, and it follows that the magnitude in radians of one complete revolution is the length of the entire circumference divided by the radius, or 2πr / r, or 2π. Thus 2π radians is equal to 360 degrees, meaning that one radian is equal to 180/π degrees, the concept of radian measure, as opposed to the degree of an angle, is normally credited to Roger Cotes in 1714. He described the radian in everything but name, and he recognized its naturalness as a unit of angular measure, the idea of measuring angles by the length of the arc was already in use by other mathematicians. For example, al-Kashi used so-called diameter parts as units where one part was 1/60 radian. The term radian first appeared in print on 5 June 1873, in examination questions set by James Thomson at Queens College, Belfast. He had used the term as early as 1871, while in 1869, Thomas Muir, then of the University of St Andrews, in 1874, after a consultation with James Thomson, Muir adopted radian. As stated, one radian is equal to 180/π degrees, thus, to convert from radians to degrees, multiply by 180/π. The length of circumference of a circle is given by 2 π r, so, to convert from radians to gradians multiply by 200 / π, and to convert from gradians to radians multiply by π /200. This is because radians have a mathematical naturalness that leads to a more elegant formulation of a number of important results, most notably, results in analysis involving trigonometric functions are simple and elegant when the functions arguments are expressed in radians. Because of these and other properties, the trigonometric functions appear in solutions to problems that are not obviously related to the functions geometrical meanings
40.
Kelvin
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The kelvin is a unit of measure for temperature based upon an absolute scale. It is one of the seven units in the International System of Units and is assigned the unit symbol K. The kelvin is defined as the fraction 1⁄273.16 of the temperature of the triple point of water. In other words, it is defined such that the point of water is exactly 273.16 K. The Kelvin scale is named after the Belfast-born, Glasgow University engineer and physicist William Lord Kelvin, unlike the degree Fahrenheit and degree Celsius, the kelvin is not referred to or typeset as a degree. The kelvin is the unit of temperature measurement in the physical sciences, but is often used in conjunction with the Celsius degree. The definition implies that absolute zero is equivalent to −273.15 °C, Kelvin calculated that absolute zero was equivalent to −273 °C on the air thermometers of the time. This absolute scale is known today as the Kelvin thermodynamic temperature scale, when spelled out or spoken, the unit is pluralised using the same grammatical rules as for other SI units such as the volt or ohm. When reference is made to the Kelvin scale, the word kelvin—which is normally a noun—functions adjectivally to modify the noun scale and is capitalized, as with most other SI unit symbols there is a space between the numeric value and the kelvin symbol. Before the 13th CGPM in 1967–1968, the unit kelvin was called a degree and it was distinguished from the other scales with either the adjective suffix Kelvin or with absolute and its symbol was °K. The latter term, which was the official name from 1948 until 1954, was ambiguous since it could also be interpreted as referring to the Rankine scale. Before the 13th CGPM, the form was degrees absolute. The 13th CGPM changed the name to simply kelvin. Its measured value was 0.01028 °C with an uncertainty of 60 µK, the use of SI prefixed forms of the degree Celsius to express a temperature interval has not been widely adopted. In 2005 the CIPM embarked on a program to redefine the kelvin using a more experimentally rigorous methodology, the current definition as of 2016 is unsatisfactory for temperatures below 20 K and above 1300 K. In particular, the committee proposed redefining the kelvin such that Boltzmanns constant takes the exact value 1. 3806505×10−23 J/K, from a scientific point of view, this will link temperature to the rest of SI and result in a stable definition that is independent of any particular substance. From a practical point of view, the redefinition will pass unnoticed, the kelvin is often used in the measure of the colour temperature of light sources. Colour temperature is based upon the principle that a black body radiator emits light whose colour depends on the temperature of the radiator, black bodies with temperatures below about 4000 K appear reddish, whereas those above about 7500 K appear bluish
41.
Megabyte
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The megabyte is a multiple of the unit byte for digital information. Its recommended unit symbol is MB, but sometimes MByte is used, the unit prefix mega is a multiplier of 1000000 in the International System of Units. Therefore, one megabyte is one million bytes of information and this definition has been incorporated into the International System of Quantities. However, in the computer and information fields, several other definitions are used that arose for historical reasons of convenience. A common usage has been to one megabyte as 1048576bytes. However, most standards bodies have deprecated this usage in favor of a set of binary prefixes, less common is a convention that used the megabyte to mean 1000×1024 bytes. The megabyte is commonly used to measure either 10002 bytes or 10242 bytes, the interpretation of using base 1024 originated as a compromise technical jargon for the byte multiples that needed to be expressed by the powers of 2 but lacked a convenient name. As 1024 approximates 1000, roughly corresponding to the SI prefix kilo-, in 1998 the International Electrotechnical Commission proposed standards for binary prefixes requiring the use of megabyte to strictly denote 10002 bytes and mebibyte to denote 10242 bytes. By the end of 2009, the IEC Standard had been adopted by the IEEE, EU, ISO, the Mac OS X10.6 file manager is a notable example of this usage in software. Since Snow Leopard, file sizes are reported in decimal units, base 21 MB =1048576 bytes is the definition used by Microsoft Windows in reference to computer memory, such as RAM. This definition is synonymous with the binary prefix mebibyte. Mixed 1 MB =1024000 bytes is the used to describe the formatted capacity of the 1.44 MB3. 5inch HD floppy disk. Semiconductor memory doubles in size for each address lane added to an integrated circuit package, the capacity of a disk drive is the product of the sector size, number of sectors per track, number of tracks per side, and the number of disk platters in the drive. Changes in any of these factors would not usually double the size, sector sizes were set as powers of two for convenience in processing. It was an extension to give the capacity of a disk drive in multiples of the sector size, giving a mix of decimal. Depending on compression methods and file format, a megabyte of data can roughly be, a 4 megapixel JPEG image with normal compression. Approximately 1 minute of 128 kbit/s MP3 compressed music,6 seconds of uncompressed CD audio. A typical English book volume in plain text format, the human genome consists of DNA representing 800 MB of data
42.
Decibel
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The decibel is a logarithmic unit used to express the ratio of two values of a physical quantity. One of these values is often a reference value, in which case the decibel is used to express the level of the other value relative to this reference. When used in way, the decibel symbol is often qualified with a suffix that indicates the reference quantity that has been used or some other property of the quantity being measured. For example, dBm indicates a power of one milliwatt. There are two different scales used when expressing a ratio in decibels depending on the nature of the quantities, when expressing power quantities, the number of decibels is ten times the logarithm to base 10 of the ratio of two power quantities. That is, a change in power by a factor of 10 corresponds to a 10 dB change in level, when expressing field quantities, a change in amplitude by a factor of 10 corresponds to a 20 dB change in level. The difference in scales relates to the square law of fields in three-dimensional linear space. The decibel scales differ so that comparisons can be made between related power and field quantities when they are expressed in decibels. The definition of the decibel is based on the measurement of power in telephony of the early 20th century in the Bell System in the United States. One decibel is one tenth of one bel, named in honor of Alexander Graham Bell, however, today, the decibel is used for a wide variety of measurements in science and engineering, most prominently in acoustics, electronics, and control theory. In electronics, the gains of amplifiers, attenuation of signals, the decibel originates from methods used to quantify signal loss in telegraph and telephone circuits. The unit for loss was originally Miles of Standard Cable, the standard telephone cable implied was a cable having uniformly distributed resistance of 88 ohms per loop mile and uniformly distributed shunt capacitance of 0.054 microfarad per mile. 1 TU was defined such that the number of TUs was ten times the logarithm of the ratio of measured power to a reference power level. The definition was conveniently chosen such that 1 TU approximated 1 MSC, in 1928, the Bell system renamed the TU into the decibel, being one tenth of a newly defined unit for the base-10 logarithm of the power ratio. It was named the bel, in honor of the telecommunications pioneer Alexander Graham Bell, the bel is seldom used, as the decibel was the proposed working unit. However, the decibel is recognized by international bodies such as the International Electrotechnical Commission. The term field quantity is deprecated by ISO 80000-1, which favors root-power, in spite of their widespread use, suffixes are not recognized by the IEC or ISO. The ISO Standard 80000-3,2006 defines the following quantities, the decibel is one-tenth of a bel,1 dB =0.1 B
43.
Imperial units
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The system of imperial units or the imperial system is the system of units first defined in the British Weights and Measures Act of 1824, which was later refined and reduced. The Imperial units replaced the Winchester Standards, which were in effect from 1588 to 1825, the system came into official use across the British Empire. The imperial system developed from what were first known as English units, the Weights and Measures Act of 1824 was initially scheduled to go into effect on 1 May 1825. However, the Weights and Measures Act of 1825 pushed back the date to 1 January 1826, the 1824 Act allowed the continued use of pre-imperial units provided that they were customary, widely known, and clearly marked with imperial equivalents. Apothecaries units are mentioned neither in the act of 1824 nor 1825, at the time, apothecaries weights and measures were regulated in England, Wales, and Berwick-upon-Tweed by the London College of Physicians, and in Ireland by the Dublin College of Physicians. In Scotland, apothecaries units were unofficially regulated by the Edinburgh College of Physicians, the three colleges published, at infrequent intervals, pharmacopoeiae, the London and Dublin editions having the force of law. The Medical Act of 1858 transferred to The Crown the right to publish the official pharmacopoeia and to regulate apothecaries weights, Metric equivalents in this article usually assume the latest official definition. Before this date, the most precise measurement of the imperial Standard Yard was 0.914398416 metres, in 1824, the various different gallons in use in the British Empire were replaced by the imperial gallon, a unit close in volume to the ale gallon. It was originally defined as the volume of 10 pounds of distilled water weighed in air with brass weights with the standing at 30 inches of mercury at a temperature of 62 °F. The Weights and Measures Act of 1985 switched to a gallon of exactly 4.54609 l and these measurements were in use from 1826, when the new imperial gallon was defined, but were officially abolished in the United Kingdom on 1 January 1971. In the USA, though no longer recommended, the system is still used occasionally in medicine. The troy pound was made the unit of mass by the 1824 Act, however, its use was abolished in the UK on 1 January 1879, with only the troy ounce. The Weights and Measures Act 1855 made the pound the primary unit of mass. In all the systems, the unit is the pound. For the yard, the length of a pendulum beating seconds at the latitude of Greenwich at Mean Sea Level in vacuo was defined as 39.01393 inches, the imperial system is one of many systems of English units. Although most of the units are defined in more than one system, some units were used to a much greater extent, or for different purposes. The distinctions between these systems are not drawn precisely. One such distinction is that between these systems and older British/English units/systems or newer additions, the US customary system is historically derived from the English units that were in use at the time of settlement
44.
United States customary units
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United States customary units are a system of measurements commonly used in the United States. The United States customary system developed from English units which were in use in the British Empire before the US declared its independence, however, the British system of measures was overhauled in 1824 to create the imperial system, changing the definitions of some units. Therefore, while many U. S. units are similar to their Imperial counterparts. The majority of U. S. customary units were redefined in terms of the meter and these definitions were refined by the international yard and pound agreement of 1959. Americans primarily use customary units in commercial activities, as well as for personal and social use, in science, medicine, many sectors of industry and some of government, metric units are used. The International System of Units, the form of the metric system, is preferred for many uses by the U. S. National Institute of Standards. The United States system of units is similar to the British imperial system, both systems are derived from English units, a system which had evolved over the millennia before American independence, and which had its roots in Roman and Anglo-Saxon units. The customary system was championed by the U. S. -based International Institute for Preserving and Perfecting Weights, advocates of the customary system saw the French Revolutionary, or metric, system as atheistic. An auxiliary of the Institute in Ohio published a poem with wording such as down with every metric scheme and A perfect inch, one adherent of the customary system called it a just weight and a just measure, which alone are acceptable to the Lord. The U. S. government passed the Metric Conversion Act of 1975, the legislation states that the federal government has a responsibility to assist industry as it voluntarily converts to the metric system, i. e. metrification. This is most evident in U. S. labeling requirements on food products, according to the CIA Factbook, the United States is one of three nations that have not adopted the metric system as their official system of weights and measures. U. S. customary units are used on consumer products. Metric units are standard in science, medicine, as well as many sectors of industry and government, the metric system also lacks a parallel to the foot. Frequently, however, these units designate quite different sizes, for example, the mile ranged by country from one-half to five U. S. miles, foot and pound also had varying definitions. Historically, a range of non-SI units were used in the U. S. and in Britain. This article deals only with the commonly used or officially defined in the U. S. For measuring length, the U. S. customary system uses the inch, foot, yard, and mile, since July 1,1959, these have been defined on the basis of 1 yard =0.9144 meters except for some applications in surveying. The U. S. the United Kingdom and other Commonwealth countries agreed on this definition, the NAD27 was replaced in the 1980s by the North American Datum of 1983, which is defined in meters
45.
Megaelectronvolt
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In physics, the electronvolt is a unit of energy equal to approximately 1. 6×10−19 joules. By definition, it is the amount of energy gained by the charge of an electron moving across an electric potential difference of one volt. Thus it is 1 volt multiplied by the elementary charge, therefore, one electronvolt is equal to 6981160217662079999♠1. 6021766208×10−19 J. The electronvolt is not a SI unit, and its definition is empirical, like the elementary charge on which it is based, it is not an independent quantity but is equal to 1 J/C √2hα / μ0c0. It is a unit of energy within physics, widely used in solid state, atomic, nuclear. It is commonly used with the metric prefixes milli-, kilo-, in some older documents, and in the name Bevatron, the symbol BeV is used, which stands for billion electronvolts, it is equivalent to the GeV. By mass–energy equivalence, the electronvolt is also a unit of mass and it is common in particle physics, where units of mass and energy are often interchanged, to express mass in units of eV/c2, where c is the speed of light in vacuum. It is common to express mass in terms of eV as a unit of mass. The mass equivalent of 1 eV/c2 is 1 eV / c 2 = ⋅1 V2 =1.783 ×10 −36 kg. For example, an electron and a positron, each with a mass of 0.511 MeV/c2, the proton has a mass of 0.938 GeV/c2. In general, the masses of all hadrons are of the order of 1 GeV/c2, the unified atomic mass unit,1 gram divided by Avogadros number, is almost the mass of a hydrogen atom, which is mostly the mass of the proton. To convert to megaelectronvolts, use the formula,1 u =931.4941 MeV/c2 =0.9314941 GeV/c2, in high-energy physics, the electronvolt is often used as a unit of momentum. A potential difference of 1 volt causes an electron to gain an amount of energy and this gives rise to usage of eV as units of momentum, for the energy supplied results in acceleration of the particle. The dimensions of units are LMT−1. The dimensions of units are L2MT−2. Then, dividing the units of energy by a constant that has units of velocity. In the field of particle physics, the fundamental velocity unit is the speed of light in vacuum c. Thus, dividing energy in eV by the speed of light, the fundamental velocity constant c is often dropped from the units of momentum by way of defining units of length such that the value of c is unity
46.
Gigaparsec
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The parsec is a unit of length used to measure large distances to objects outside the Solar System. One parsec is the distance at which one astronomical unit subtends an angle of one arcsecond, a parsec is equal to about 3.26 light-years in length. The nearest star, Proxima Centauri, is about 1.3 parsecs from the Sun, most of the stars visible to the unaided eye in the nighttime sky are within 500 parsecs of the Sun. The parsec unit was likely first suggested in 1913 by the British astronomer Herbert Hall Turner, named from an abbreviation of the parallax of one arcsecond, it was defined so as to make calculations of astronomical distances quick and easy for astronomers from only their raw observational data. Partly for this reason, it is still the unit preferred in astronomy and astrophysics, though the light-year remains prominent in science texts. This corresponds to the definition of the parsec found in many contemporary astronomical references. Derivation, create a triangle with one leg being from the Earth to the Sun. As that point in space away, the angle between the Sun and Earth decreases. A parsec is the length of that leg when the angle between the Sun and Earth is one arc-second. One of the oldest methods used by astronomers to calculate the distance to a star is to record the difference in angle between two measurements of the position of the star in the sky. The first measurement is taken from the Earth on one side of the Sun, and the second is approximately half a year later. The distance between the two positions of the Earth when the two measurements were taken is twice the distance between the Earth and the Sun. The difference in angle between the two measurements is twice the angle, which is formed by lines from the Sun. Then the distance to the star could be calculated using trigonometry. 5-parsec distance of 61 Cygni, the parallax of a star is defined as half of the angular distance that a star appears to move relative to the celestial sphere as Earth orbits the Sun. Equivalently, it is the angle, from that stars perspective. The star, the Sun and the Earth form the corners of a right triangle in space, the right angle is the corner at the Sun. Therefore, given a measurement of the angle, along with the rules of trigonometry. A parsec is defined as the length of the adjacent to the vertex occupied by a star whose parallax angle is one arcsecond
47.
Year
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A year is the orbital period of the Earth moving in its orbit around the Sun. Due to the Earths axial tilt, the course of a year sees the passing of the seasons, marked by changes in weather, the hours of daylight, and, consequently, vegetation and soil fertility. In temperate and subpolar regions around the globe, four seasons are recognized, spring, summer, autumn. In tropical and subtropical regions several geographical sectors do not present defined seasons, but in the seasonal tropics, a calendar year is an approximation of the number of days of the Earths orbital period as counted in a given calendar. The Gregorian, or modern, calendar, presents its calendar year to be either a common year of 365 days or a year of 366 days, as do the Julian calendars. For the Gregorian calendar the average length of the year across the complete leap cycle of 400 years is 365.2425 days. The ISO standard ISO 80000-3, Annex C, supports the symbol a to represent a year of either 365 or 366 days, in English, the abbreviations y and yr are commonly used. In astronomy, the Julian year is a unit of time, it is defined as 365.25 days of exactly 86400 seconds, totalling exactly 31557600 seconds in the Julian astronomical year. The word year is used for periods loosely associated with, but not identical to, the calendar or astronomical year, such as the seasonal year, the fiscal year. Similarly, year can mean the period of any planet, for example. The term can also be used in reference to any long period or cycle, west Saxon ġēar, Anglian ġēr continues Proto-Germanic *jǣran. Cognates are German Jahr, Old High German jār, Old Norse ár and Gothic jer, all the descendants of the Proto-Indo-European noun *yeh₁rom year, season. Cognates also descended from the same Proto-Indo-European noun are Avestan yārǝ year, Greek ὥρα year, season, period of time, Old Church Slavonic jarŭ, Latin annus is from a PIE noun *h₂et-no-, which also yielded Gothic aþn year. Both *yeh₁-ro- and *h₂et-no- are based on verbal roots expressing movement, *h₁ey- and *h₂et- respectively, the Greek word for year, ἔτος, is cognate with Latin vetus old, from the PIE word *wetos- year, also preserved in this meaning in Sanskrit vat-sa- yearling and vat-sa-ras year. Derived from Latin annus are a number of English words, such as annual, annuity, anniversary, etc. per annum means each year, anno Domini means in the year of the Lord. No astronomical year has an number of days or lunar months. Financial and scientific calculations often use a 365-day calendar to simplify daily rates, in the Julian calendar, the average length of a year is 365.25 days. In a non-leap year, there are 365 days, in a year there are 366 days
48.
Kiloannus
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A year is the orbital period of the Earth moving in its orbit around the Sun. Due to the Earths axial tilt, the course of a year sees the passing of the seasons, marked by changes in weather, the hours of daylight, and, consequently, vegetation and soil fertility. In temperate and subpolar regions around the globe, four seasons are recognized, spring, summer, autumn. In tropical and subtropical regions several geographical sectors do not present defined seasons, but in the seasonal tropics, a calendar year is an approximation of the number of days of the Earths orbital period as counted in a given calendar. The Gregorian, or modern, calendar, presents its calendar year to be either a common year of 365 days or a year of 366 days, as do the Julian calendars. For the Gregorian calendar the average length of the year across the complete leap cycle of 400 years is 365.2425 days. The ISO standard ISO 80000-3, Annex C, supports the symbol a to represent a year of either 365 or 366 days, in English, the abbreviations y and yr are commonly used. In astronomy, the Julian year is a unit of time, it is defined as 365.25 days of exactly 86400 seconds, totalling exactly 31557600 seconds in the Julian astronomical year. The word year is used for periods loosely associated with, but not identical to, the calendar or astronomical year, such as the seasonal year, the fiscal year. Similarly, year can mean the period of any planet, for example. The term can also be used in reference to any long period or cycle, west Saxon ġēar, Anglian ġēr continues Proto-Germanic *jǣran. Cognates are German Jahr, Old High German jār, Old Norse ár and Gothic jer, all the descendants of the Proto-Indo-European noun *yeh₁rom year, season. Cognates also descended from the same Proto-Indo-European noun are Avestan yārǝ year, Greek ὥρα year, season, period of time, Old Church Slavonic jarŭ, Latin annus is from a PIE noun *h₂et-no-, which also yielded Gothic aþn year. Both *yeh₁-ro- and *h₂et-no- are based on verbal roots expressing movement, *h₁ey- and *h₂et- respectively, the Greek word for year, ἔτος, is cognate with Latin vetus old, from the PIE word *wetos- year, also preserved in this meaning in Sanskrit vat-sa- yearling and vat-sa-ras year. Derived from Latin annus are a number of English words, such as annual, annuity, anniversary, etc. per annum means each year, anno Domini means in the year of the Lord. No astronomical year has an number of days or lunar months. Financial and scientific calculations often use a 365-day calendar to simplify daily rates, in the Julian calendar, the average length of a year is 365.25 days. In a non-leap year, there are 365 days, in a year there are 366 days
49.
LaTeX
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LaTeX is a document preparation system. When writing, the writer uses plain text as opposed to the text found in WYSIWYG word processors like Microsoft Word or LibreOffice Writer. The writer uses markup tagging conventions to define the structure of a document, to stylise text throughout a document. A TeX distribution such as TeX Live or MikTeX is used to produce a file suitable for printing or digital distribution. Within the typesetting system, its name is stylised as LaTeX and it also has a prominent role in the preparation and publication of books and articles that contain complex multilingual materials, such as Tamil, Sanskrit and Greek. LaTeX uses the TeX typesetting program for formatting its output, LaTeX can be used as a standalone document preparation system or as an intermediate format. In the latter role, for example, it is used as part of a pipeline for translating DocBook. LaTeX is intended to provide a language that accesses the power of TeX in an easier way for writers. In short, TeX handles the layout side, while LaTeX handles the content side for document processing, LaTeX comprises a collection of TeX macros and a program to process LaTeX documents. LaTeX was originally written in the early 1980s by Leslie Lamport at SRI International, LaTeX is free software and is distributed under the LaTeX Project Public License. It therefore encourages the separation of layout from content while still allowing manual typesetting adjustments where needed and this concept is similar to the mechanism by which many word processors allow styles to be defined globally for an entire document or the use of Cascading Style Sheets to style HTML. The LaTeX system is a language that also handles typesetting and rendering. LaTeX can be extended by using the underlying macro language to develop custom formats. Such macros are often collected into packages, which are available to address special formatting such as complicated mathematical content or graphics. Indeed, in the example below, the environment is provided by the amsmath package. In order to create a document in LaTeX, you first write a file, say document. tex, then you give your document. tex file as input to the TeX program, and TeX writes out a file suitable for viewing onscreen or printing. This write-format-preview cycle is one of the ways in which working with LaTeX differs from what-you-see-is-what-you-get word-processing. It is similar to the code-compile-execute cycle familiar to computer programmers, today, many LaTeX-aware editing programs make this cycle a simple matter of pressing a single key, while showing the output preview on the screen beside the input window
50.
Rhine
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The largest city on the river Rhine is Cologne, Germany, with a population of more than 1,050,000 people. It is the second-longest river in Central and Western Europe, at about 1,230 km, with an average discharge of about 2,900 m3/s. The Rhine and the Danube formed most of the inland frontier of the Roman Empire and, since those days. The many castles and fortifications along the Rhine testify to its importance as a waterway in the Holy Roman Empire, in the modern era, it has become a symbol of German nationalism. The variant of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-. The Gaulish name Rēnos belongs to a class of river names built from the PIE root *rei- to move, flow, run, the grammatical gender of the Celtic name is masculine, and the name remains masculine in German, Dutch and French. The Old English river name was variously inflected as masculine or feminine, the length of the Rhine is conventionally measured in Rhine-kilometers, a scale introduced in 1939 which runs from the Old Rhine Bridge at Constance to Hoek van Holland. The river length is shortened from the rivers natural course due to a number of canalisation projects completed in the 19th and 20th century. The total length of the Rhine, to the inclusion of Lake Constance and its course is conventionally divided as follows, The Rhine carries its name without distinctive accessories only from the confluence of the Vorderrhein and Hinterrhein near Tamins-Reichenau. Above this point is the catchment of the headwaters of the Rhine. It belongs almost exclusively to the Swiss Canton of Graubünden, ranging from Gotthard Massif in the west via one valley lying in Ticino, traditionally, Lake Toma near the Oberalp Pass in the Gotthard region is seen as the source of the Vorderrhein and the Rhine as a whole. The Hinterrhein rises in the Rheinwald valley below Mount Rheinwaldhorn, the Vorderrhein, or Anterior Rhine, springs from Lai da Tuma, near the Oberalp Pass and passes the impressive Ruinaulta formed by the largest visible rock slide in the alps, the Flims Rockslide. A multiday trekking route is signposted along the young Rhine called Senda Sursilvana, the Hinterrhein/Rein Posteriur, or Posterior Rhine, starts from the Paradies Glacier, near the Rheinwaldhorn. One of its tributaries, the Reno di Lei, drains the Valle di Lei on politically Italian territory, after three main valleys separated by the two gorges, Roflaschlucht and Viamala, it reaches Reichenau. The Vorderrhein arises from numerous source streams in the upper Surselva, one source is Lai da Tuma with the Rein da Tuma, which is usually indicated as source of the Rhine, flowing through it. Into it flow tributaries from the south, some longer, some equal in length, such as the Reno di Medel, the Rein da Maighels, and the Rein da Curnera. The Cadlimo Valley in the Canton of Ticino is drained by the Reno di Medel, all streams in the source area are partially, sometimes completely, captured and sent to storage reservoirs for the local hydro-electric power plants. In its lower course the Vorderrhein flows through a gorge named Ruinaulta through the Flims Rockslide, the whole stretch of the Vorderrhein to the Rhine confluence near Reichenau-Tamins is accompanied by a long-distance hiking trail called Senda Sursilvana
51.
Basel
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Basel is a city in northwestern Switzerland on the river Rhine. Basel is Switzerlands third-most-populous city with about 175,000 inhabitants, located where the Swiss, French and German borders meet, Basel also has suburbs in France and Germany. In 2014, the Basel agglomeration was the third largest in Switzerland with a population of 537,100 in 74 municipalities in Switzerland, the official language of Basel is German, but the main spoken language is the local variant of the Alemannic Swiss German dialect. Basel has been the seat of a Prince-Bishopric since the 11th century, the city has been a commercial hub and important cultural centre since the Renaissance, and has emerged as a centre for the chemical and pharmaceutical industry in the 20th century. It hosts the oldest university of the Swiss Confederation, There are settlement traces on the Rhine knee from the early La Tène period. The unfortified settlement was abandoned in the 1st century BC in favour of an Oppidum on the site of Basel Minster, probably in reaction to the Roman invasion of Gaul. In Roman Gaul, Augusta Raurica was established some 20 km from Basel as the administrative centre. The city of Basel eventually grew around the castle, the name of Basel is derived from the Roman-era toponym Basilia, first recorded in the 3rd century. It is presumably derived from the personal name Basilius, the Old French form Basle was adopted into English, and developed into the modern French Bâle. The Icelandic name Buslaraborg goes back to the 12th century Leiðarvísir og borgarskipan, Basel was incorporated into Germania Superior in AD83. Roman control over the area deteriorated in 3rd century, and Basel became an outpost of the Provincia Maxima Sequanorum formed by Diocletian, the Alamanni attempted to cross the Rhine several times in the 4th century, but were repelled. In a great invasion of AD406, the Alemanni appear to have crossed the Rhine river a final time, conquering and then settling what is today Alsace, from this time, Basel has been an Alemannic settlement. The Duchy of Alemannia fell under Frankish rule in the 6th century, and by the 7th century, based on the evidence of a third solidus with the inscription Basilia fit, Basel seems to have minted its own coins in the 7th century. Under bishop Haito, the first cathedral was built on the site of the Roman castle, at the partition of the Carolingian Empire, Basel was first given to West Francia, but passed to East Francia with the treaty of Meerssen of 870. The city was plundered and destroyed by a Magyar invasion of 917, the rebuilt city became part of Upper Burgundy, and as such was incorporated into the Holy Roman Empire in 1032. Since the donation by Rudolph III of Burgundy of the Moutier-Grandval Abbey and all its possessions to Bishop Adalbero II in 999 till the Reformation, in 1019, the construction of the cathedral of Basel began under German Emperor Heinrich II. In 1225–1226, the Bridge over the Rhine was constructed by Bishop Heinrich von Thun, the bridge was largely funded by Basels Jewish community which had settled there a century earlier. For many centuries to come Basel possessed the only permanent bridge over the river between Lake Constance and the sea, the Bishop also allowed the furriers to found a guild in 1226
52.
Decimal mark
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A decimal mark is a symbol used to separate the integer part from the fractional part of a number written in decimal form. Different countries officially designate different symbols for the decimal mark, the choice of symbol for the decimal mark also affects the choice of symbol for the thousands separator used in digit grouping, so the latter is also treated in this article. In mathematics the decimal mark is a type of radix point, in the Middle Ages, before printing, a bar over the units digit was used to separate the integral part of a number from its fractional part, e. g.9995. His Compendious Book on Calculation by Completion and Balancing presented the first systematic solution of linear, a similar notation remains in common use as an underbar to superscript digits, especially for monetary values without a decimal mark, e. g.9995. Later, a separatrix between the units and tenths position became the norm among Arab mathematicians, e. g. 99ˌ95, when this character was typeset, it was convenient to use the existing comma or full stop instead. The separatrix was also used in England as an L-shaped or vertical bar before the popularization of the period, gerbert of Aurillac marked triples of columns with an arc when using his Hindu–Arabic numeral-based abacus in the 10th century. Fibonacci followed this convention when writing numbers such as in his influential work Liber Abaci in the 13th century, in France, the full stop was already in use in printing to make Roman numerals more readable, so the comma was chosen. Many other countries, such as Italy, also chose to use the comma to mark the decimal units position and it has been made standard by the ISO for international blueprints. However, English-speaking countries took the comma to separate sequences of three digits, in some countries, a raised dot or dash may be used for grouping or decimal mark, this is particularly common in handwriting. In the United States, the stop or period was used as the standard decimal mark. g. However, as the mid dot was already in use in the mathematics world to indicate multiplication. In the event, the point was decided on by the Ministry of Technology in 1968, the three most spoken international auxiliary languages, Ido, Esperanto, and Interlingua, all use the comma as the decimal mark. Interlingua has used the comma as its decimal mark since the publication of the Interlingua Grammar in 1951, Esperanto also uses the comma as its official decimal mark, while thousands are separated by non-breaking spaces,12345678,9. Idos Kompleta Gramatiko Detaloza di la Linguo Internaciona Ido officially states that commas are used for the mark while full stops are used to separate thousands, millions. So the number 12,345,678.90123 for instance, the 1931 grammar of Volapük by Arie de Jong uses the comma as its decimal mark, and uses the middle dot as the thousands separator. In 1958, disputes between European and American delegates over the representation of the decimal mark nearly stalled the development of the ALGOL computer programming language. ALGOL ended up allowing different decimal marks, but most computer languages, the 22nd General Conference on Weights and Measures declared in 2003 that the symbol for the decimal marker shall be either the point on the line or the comma on the line. It further reaffirmed that numbers may be divided in groups of three in order to facilitate reading, neither dots nor commas are ever inserted in the spaces between groups
53.
Germany
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Germany, officially the Federal Republic of Germany, is a federal parliamentary republic in central-western Europe. It includes 16 constituent states, covers an area of 357,021 square kilometres, with about 82 million inhabitants, Germany is the most populous member state of the European Union. After the United States, it is the second most popular destination in the world. Germanys capital and largest metropolis is Berlin, while its largest conurbation is the Ruhr, other major cities include Hamburg, Munich, Cologne, Frankfurt, Stuttgart, Düsseldorf and Leipzig. Various Germanic tribes have inhabited the northern parts of modern Germany since classical antiquity, a region named Germania was documented before 100 AD. During the Migration Period the Germanic tribes expanded southward, beginning in the 10th century, German territories formed a central part of the Holy Roman Empire. During the 16th century, northern German regions became the centre of the Protestant Reformation, in 1871, Germany became a nation state when most of the German states unified into the Prussian-dominated German Empire. After World War I and the German Revolution of 1918–1919, the Empire was replaced by the parliamentary Weimar Republic, the establishment of the national socialist dictatorship in 1933 led to World War II and the Holocaust. After a period of Allied occupation, two German states were founded, the Federal Republic of Germany and the German Democratic Republic, in 1990, the country was reunified. In the 21st century, Germany is a power and has the worlds fourth-largest economy by nominal GDP. As a global leader in industrial and technological sectors, it is both the worlds third-largest exporter and importer of goods. Germany is a country with a very high standard of living sustained by a skilled. It upholds a social security and universal health system, environmental protection. Germany was a member of the European Economic Community in 1957. It is part of the Schengen Area, and became a co-founder of the Eurozone in 1999, Germany is a member of the United Nations, NATO, the G8, the G20, and the OECD. The national military expenditure is the 9th highest in the world, the English word Germany derives from the Latin Germania, which came into use after Julius Caesar adopted it for the peoples east of the Rhine. This in turn descends from Proto-Germanic *þiudiskaz popular, derived from *þeudō, descended from Proto-Indo-European *tewtéh₂- people, the discovery of the Mauer 1 mandible shows that ancient humans were present in Germany at least 600,000 years ago. The oldest complete hunting weapons found anywhere in the world were discovered in a mine in Schöningen where three 380, 000-year-old wooden javelins were unearthed
54.
Myria-
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Myria- is a now obsolete decimal metric prefix equal to 104. It originates from the Greek μύριοι, the prefix was part of the original metric system adopted by France in 1795, but was not adopted when the SI prefixes were internationally adopted by the 11th CGPM conference in 1960. In 1685 John Wallis proposed the usage of myrio, also, in 19th century English it was sometimes spelled myrio, in line with a puristic opinion by Thomas Young. The myriametre is occasionally encountered in 19th-century train tariffs, or in some classifications of wavelengths as the adjective myriametric, the French mesures usuelles did not include any units of length greater than the toise, but the myriametre remained in use throughout this period. In Sweden and Norway, the myriametre is still common in everyday use, in these countries this unit is called mil. Of units customarily used in trade in France, the myriagramme was the replacement for an avoirdupois unit. Isaac Asimovs novel Foundation and Empire still mentioned the myriaton in 1952, the myria’s symbol of my ultimately led to its demise. In 1905 the Comité International des Poids et Mesures assigned it the symbol M and this meant that myriameter, for example, was abbreviated Mm. But in the first part of the century, electrical engineers began to use capital M for the prefix mega-, as in megawatt. This usage became so widely and firmly adopted that in 1935 the CIPM adopted the prefix “mega-” with “M” as its symbol, in 1975, the United States, having previously authorized use of the myriameter and myriagram in 1866, declared the terms no longer acceptable. Myriagon Myriapoda dimi- (aka decimilli-, a former French metric prefix denoting the inverse of the prefix up to 1961 Obsolete metric prefix
55.
Myrio-
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Myria- is a now obsolete decimal metric prefix equal to 104. It originates from the Greek μύριοι, the prefix was part of the original metric system adopted by France in 1795, but was not adopted when the SI prefixes were internationally adopted by the 11th CGPM conference in 1960. In 1685 John Wallis proposed the usage of myrio, also, in 19th century English it was sometimes spelled myrio, in line with a puristic opinion by Thomas Young. The myriametre is occasionally encountered in 19th-century train tariffs, or in some classifications of wavelengths as the adjective myriametric, the French mesures usuelles did not include any units of length greater than the toise, but the myriametre remained in use throughout this period. In Sweden and Norway, the myriametre is still common in everyday use, in these countries this unit is called mil. Of units customarily used in trade in France, the myriagramme was the replacement for an avoirdupois unit. Isaac Asimovs novel Foundation and Empire still mentioned the myriaton in 1952, the myria’s symbol of my ultimately led to its demise. In 1905 the Comité International des Poids et Mesures assigned it the symbol M and this meant that myriameter, for example, was abbreviated Mm. But in the first part of the century, electrical engineers began to use capital M for the prefix mega-, as in megawatt. This usage became so widely and firmly adopted that in 1935 the CIPM adopted the prefix “mega-” with “M” as its symbol, in 1975, the United States, having previously authorized use of the myriameter and myriagram in 1866, declared the terms no longer acceptable. Myriagon Myriapoda dimi- (aka decimilli-, a former French metric prefix denoting the inverse of the prefix up to 1961 Obsolete metric prefix
56.
Binary prefix
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A binary prefix is a unit prefix for multiples of units in data processing, data transmission, and digital information, notably the bit and the byte, to indicate multiplication by a power of 2. The computer industry has used the units kilobyte, megabyte, and gigabyte, and the corresponding symbols KB, MB. In citations of main memory capacity, gigabyte customarily means 1073741824 bytes, as this is the third power of 1024, and 1024 is a power of two, this usage is referred to as a binary measurement. In most other contexts, the uses the multipliers kilo, mega, giga, etc. in a manner consistent with their meaning in the International System of Units. For example, a 500 gigabyte hard disk holds 500000000000 bytes, in contrast with the binary prefix usage, this use is described as a decimal prefix, as 1000 is a power of 10. The use of the same unit prefixes with two different meanings has caused confusion, in 2008, the IEC prefixes were incorporated into the ISO/IEC80000 standard. Early computers used one of two addressing methods to access the memory, binary or decimal. For example, the IBM701 used binary and could address 2048 words of 36 bits each, while the IBM702 used decimal, by the mid-1960s, binary addressing had become the standard architecture in most computer designs, and main memory sizes were most commonly powers of two. Early computer system documentation would specify the size with an exact number such as 4096,8192. These are all powers of two, and furthermore are small multiples of 210, or 1024, as storage capacities increased, several different methods were developed to abbreviate these quantities. The method most commonly used today uses prefixes such as kilo, mega, giga, and corresponding symbols K, M, and G, the prefixes kilo- and mega-, meaning 1000 and 1000000 respectively, were commonly used in the electronics industry before World War II. Along with giga- or G-, meaning 1000000000, they are now known as SI prefixes after the International System of Units, introduced in 1960 to formalize aspects of the metric system. The International System of Units does not define units for digital information and this usage is not consistent with the SI. Compliance with the SI requires that the prefixes take their 1000-based meaning, the use of K in the binary sense as in a 32K core meaning 32 ×1024 words, i. e.32768 words, can be found as early as 1959. Gene Amdahls seminal 1964 article on IBM System/360 used 1K to mean 1024 and this style was used by other computer vendors, the CDC7600 System Description made extensive use of K as 1024. Thus the first binary prefix was born, the exact values 32768 words,65536 words and 131072 words would then be described as 32K, 65K and 131K. This style was used from about 1965 to 1975 and these two styles were used loosely around the same time, sometimes by the same company. In discussions of binary-addressed memories, the size was evident from context
57.
One half
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One half is the irreducible fraction resulting from dividing one by two, or the fraction resulting from dividing any number by its double. Multiplication by one half is equivalent to division by two, or halving, conversely, division by one half is equivalent to multiplication by two, or doubling, one half appears often in mathematical equations, recipes, measurements, etc. Half can also be said to be one part of something divided into two equal parts, for instance, the area S of a triangle is computed S = 1⁄2 × base × perpendicular height. The Riemann hypothesis states that every nontrivial complex root of the Riemann zeta function has a part equal to 1⁄2. One half has two different decimal expansions, the familiar 0.5 and the recurring 0.49999999 and it has a similar pair of expansions in any even base. It is a trap to believe these expressions represent distinct numbers. Equals 1 for detailed discussion of a related case, in odd bases, one half has no terminating representation, only a single representation with a repeating fractional component, such as 0.11111111. in ternary. 1⁄2 is also one of the few fractions to usually have a key of its own on typewriters and it also has its own code point in some early extensions of ASCII at 171. In Unicode, it has its own unit at U+00BD in the C1 Controls and Latin-1 Supplement block. List of numbers Division by two