1.
Hectare
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The hectare is an SI accepted metric system unit of area equal to 100 ares and primarily used in the measurement of land as a metric replacement for the imperial acre. An acre is about 0.405 hectare and one hectare contains about 2.47 acres, in 1795, when the metric system was introduced, the are was defined as 100 square metres and the hectare was thus 100 ares or 1⁄100 km2. When the metric system was further rationalised in 1960, resulting in the International System of Units, the are was not included as a recognised unit. The hectare, however, remains as a non-SI unit accepted for use with the SI units, the metric system of measurement was first given a legal basis in 1795 by the French Revolutionary government. At the first meeting of the CGPM in 1889 when a new standard metre, manufactured by Johnson Matthey & Co of London was adopted, in 1960, when the metric system was updated as the International System of Units, the are did not receive international recognition. The units that were catalogued replicated the recommendations of the CGPM, many farmers, especially older ones, still use the acre for everyday calculations, and convert to hectares only for official paperwork. Farm fields can have long histories which are resistant to change, with names such as the six acre field stretching back hundreds of years. The names centiare, deciare, decare and hectare are derived by adding the standard metric prefixes to the base unit of area. The centiare is a synonym for one square metre, the deciare is ten square metres. The are is a unit of area, equal to 100 square metres and it was defined by older forms of the metric system, but is now outside of the modern International System of Units. It is commonly used to measure real estate, in particular in Indonesia, India, and in French-, Portuguese-, Slovakian-, Serbian-, Czech-, Polish-, Dutch-, in Russia and other former Soviet Union states, the are is called sotka. It is used to describe the size of suburban dacha or allotment garden plots or small city parks where the hectare would be too large, the decare is derived from deka, the prefix for 10 and are, and is equal to 10 ares or 1000 square metres. It is used in Norway and in the former Ottoman areas of the Middle East, the hectare, although not strictly a unit of SI, is the only named unit of area that is accepted for use within the SI. The United Kingdom, United States, Burma, and to some extent Canada instead use the acre, others, such as South Africa, published conversion factors which were to be used particularly when preparing consolidation diagrams by compilation. In many countries, metrication redefined or clarified existing measures in terms of metric units, non-SI units accepted for use with the International System of Units

2.
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

3.
American and British English spelling differences
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Many of the differences between American and British English date back to a time when spelling standards had not yet developed. For instance, some spellings seen as American today were once used in Britain. But English-language spelling reform has rarely been adopted otherwise, and thus modern English orthography varies somewhat between countries and is far from phonemic in any country, in the early 18th century, English spelling was inconsistent. These differences became noticeable after the publishing of influential dictionaries, todays British English spellings mostly follow Johnsons A Dictionary of the English Language, while many American English spellings follow Websters An American Dictionary of the English Language. Webster was a proponent of English spelling reform for reasons both philological and nationalistic, in A Companion to the American Revolution, John Algeo notes, it is often assumed that characteristically American spellings were invented by Noah Webster. He was very influential in popularizing certain spellings in America, rather he chose already existing options such as center, color and check for the simplicity, analogy or etymology. William Shakespeares first folios, for example, used spellings like center and color as much as centre, Webster did attempt to introduce some reformed spellings, as did the Simplified Spelling Board in the early 20th century, but most were not adopted. In Britain, the influence of those who preferred the Norman spellings of words proved to be decisive, later spelling adjustments in the United Kingdom had little effect on todays American spellings and vice versa. For the most part, the systems of most Commonwealth countries. Australian spelling has also strayed slightly from British spelling, with some American spellings incorporated as standard, New Zealand spelling is almost identical to British spelling, except in the word fiord. There is also an increasing use of macrons in words that originated in Māori, most words ending in an unstressed -our in British English end in -or in American English. Wherever the vowel is unreduced in pronunciation, e. g. contour, velour, paramour and troubadour the spelling is the same everywhere, most words of this kind came from Latin, where the ending was spelled -or. They were first adopted into English from early Old French, after the Norman conquest of England, the ending became -our to match the Old French spelling. The -our ending was not only used in new English borrowings, however, -or was still sometimes found, and the first three folios of Shakespeares plays used both spellings before they were standardised to -our in the Fourth Folio of 1685. After the Renaissance, new borrowings from Latin were taken up with their original -or ending, Websters 1828 dictionary had only -or and is given much of the credit for the adoption of this form in the United States. Johnson, unlike Webster, was not an advocate of spelling reform and he preferred French over Latin spellings because, as he put it, the French generally supplied us. In Jeffersons original draft it is spelled honour, Honor and honour were equally frequent in Britain until the 17th century, honor still is, in the UK, the usual spelling as a persons name and appears in Honor Oak, a district of London. In derivatives and inflected forms of the words, British usage depends on the nature of the suffix used

4.
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

5.
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

6.
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

7.
Metric 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

8.
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

9.
1,000,000
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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

10.
Kilometre
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The kilometre or kilometer is a unit of length in the metric system, equal to one thousand metres. K is occasionally used in some English-speaking countries as an alternative for the kilometre in colloquial writing. A slang term for the kilometre in the US military is klick, there are two common pronunciations for the word. It is generally preferred by the British Broadcasting Corporation and the Australian Broadcasting Corporation, many scientists and other users, particularly in countries where the metric system is not widely used, use the pronunciation with stress on the second syllable. The latter pronunciation follows the pattern used for the names of measuring instruments. The problem with this reasoning, however, is that the meter in those usages refers to a measuring device. The contrast is more obvious in countries using the British rather than American spelling of the word metre. When Australia introduced the system in 1975, the first pronunciation was declared official by the governments Metric Conversion Board. However, the Australian prime minister at the time, Gough Whitlam, by the 8 May 1790 decree, the Constituent assembly ordered the French Academy of Sciences to develop a new measurement system. In August 1793, the French National Convention decreed the metre as the length measurement system in the French Republic. The first name of the kilometre was Millaire, although the metre was formally defined in 1799, the myriametre was preferred to the kilometre for everyday use. The term myriamètre appeared a number of times in the text of Develeys book Physique dEmile, ou, Principes de la de la nature. French maps published in 1835 had scales showing myriametres and lieues de Poste, the Dutch, on the other hand, adopted the kilometre in 1817 but gave it the local name of the mijl. It was only in 1867 that the term became the only official unit of measure in the Netherlands to represent 1000 metres. In the US, the National Highway System Designation Act of 1995 prohibits the use of highway funds to convert existing signs or purchase new signs with metric units. Although the State DOTs had the option of using metric measurements or dual units, all of them abandoned metric measurements, the Manual on Uniform Traffic Control Devices since 2000 is published in both metric and American Customary Units. Some sporting disciplines feature 1000 m races in major events, but in other disciplines, even though records are catalogued