Metric prefix
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 common use today are decadic there have been a number of binary metric prefixes as well; each prefix has a unique symbol, prepended to the unit symbol. The prefix kilo-, for example, may be added to gram to indicate multiplication by one thousand: one kilogram is equal to one thousand grams; the prefix milli- may be added to metre to indicate division by one thousand. Decimal multiplicative prefixes have been a feature of all forms of the metric system, with six of these dating back to the system's introduction in the 1790s. Metric prefixes have been used with some 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, used in combination with the symbols for units of measure. For example, the symbol for'kilo-' is'k', is used to produce'km','kg', and'kW', which are the SI symbols for kilometre and kilowatt, respectively. Where the Greek letter'μ' is unavailable, the symbol for micro'µ' may be used. Where both variants are unavailable, the micro prefix is written as the lowercase Latin letter'u'. Prefixes corresponding to an integer power of one thousand are preferred. Hence'100 m' is preferred over'1 hm' or'10 dam'; the prefixes hecto, deca and centi are used for everyday purposes, the centimetre is common. However, some modern building codes require that the millimetre be used in preference to the centimetre, because "use of centimetres leads to extensive usage of decimal points and confusion". Prefixes may not be used in combination; this applies to mass, for which the SI base unit 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, except when combining values with identical units. Hence, 5 mV × 5 mA = 5×10−3 V × 5×10−3 A = 25×10−6 V⋅A = 25 μW 5.00 mV + 10 μV = 5.00 mV + 0.01 mV = 5.01 mVWhen powers of units occur, for example, squared or cubed, the multiplication prefix must be considered part of the unit, thus included in the exponentiation. 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, not 2000000 cubic metres. Examples5 cm = 5×10−2 m = 5 × 0.01 m = 0.05 m 9 km2 = 9 × 2 = 9 × 2 × m2 = 9×106 m2 = 9 × 1000000 m2 = 9000000 m2 3 MW = 3×106 W = 3 × 1000000 W = 3000000 W The use of prefixes can be traced back to the introduction of the metric system in the 1790s, long before the 1960 introduction of the SI. The prefixes, including those introduced after 1960, are used with any metric unit, whether included in the SI or not.
Metric prefixes may be used with non-metric units. The choice of prefixes with a given unit is dictated by convenience of use. Unit prefixes for amounts that are much larger or smaller than those encountered are used; the units kilogram, milligram and smaller are used for measurement of mass. However, megagram and larger are used. Megagram and teragram are used to disambiguate the metric tonne from other units with the name'ton'; the kilogram is the only base unit of the International System of Units that includes a metric prefix. The litre, millilitre and smaller are common. In Europe, the centilitre is used for packaged products such as wine and the decilitre is less frequently; the latter two items include prefixes corresponding to an exponent, not divisible by three. Larger volumes are denoted in kilolitres, megalitres or gigalitres, or else in cubic metres or cubic kilometres. For scientific purposes, the cubic metre is used; the kilometre, centimetre and smaller are common. The micrometre is referred to by the non-SI term micron.
In some fields, such as chemistry, the ångström competed with the nanometre. The femtometre, used in particle physics, is sometimes called a fermi. For large scales, megametre and larger are used. Instead, non-metric units are used, such as astronomical units, light years, parsecs; the second, millisecond and shorter are common. The kilosecond and megasecond have some use, though for these and longer times one uses either scientific notation or minutes, so on; the SI unit of angle is the radian, but degrees and seconds see some scientific use. Official policy varies from common practice for the degree Celsius. NIST states: "Prefix symbols may be used with the unit symbol °C and prefix names may be used with the unit name'degree Celsius'. For example, 12 m°C (12 millidegr
Kilometre
The kilometre, or kilometer is a unit of length in the metric system, equal to one thousand metres. It is now the measurement unit used for expressing distances between geographical places on land in most of the world. K is used in some English-speaking countries as an alternative for the word kilometre in colloquial writing and speech. A slang term for the kilometre in the US and UK military is klick. There are two common pronunciations for the word; the former follows a pattern in English whereby metric units are pronounced with the stress on the first syllable and the pronunciation of the actual base unit does not change irrespective of the prefix. It is preferred by the British Broadcasting Corporation and the Australian Broadcasting Corporation. Many scientists and other users in countries where the metric system is not used, use the pronunciation with stress on the second syllable; the latter pronunciation follows the stress pattern used for the names of measuring instruments. The problem with this reasoning, however, is that the word meter in those usages refers to a measuring device, not a unit of length.
The contrast is more obvious in countries using the British rather than American spelling of the word metre. When Australia introduced the metric system in 1975, the first pronunciation was declared official by the government's Metric Conversion Board. However, the Australian prime minister at the time, Gough Whitlam, insisted that the second pronunciation was the correct one because of the Greek origins of the two parts of the word. 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 sole 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 Develey's book Physique d'Emile: ou, Principes de la science de la nature, while the term kilometre only appeared in an appendix.
French maps published in 1835 had scales showing myriametres and "lieues de Poste". The Dutch gave it the local name of the mijl, it was only in 1867 that the term "kilometer" became the only official unit of measure in the Netherlands to represent 1000 metres. Two German textbooks dated 1842 and 1848 give a snapshot of the use of the kilometre across Europe - the kilometre was in use in the Netherlands and in Italy and the myriametre was in use in France. In 1935, the International Committee for Weights and Measures abolished the prefix "myria-" and with it the "myriametre", leaving the kilometre as the recognised unit of length for measurements of that magnitude. In the United Kingdom, road signs show distances in miles and location marker posts that are used for reference purposes by road engineers and emergency services show distance references in unspecified units which are kilometre-based; the advent of the mobile phone has been instrumental in the British Department for Transport authorising the use of driver location signs to convey the distance reference information of location marker posts to road users should they need to contact the emergency services.
In the US, the National Highway System Designation Act of 1995 prohibits the use of federal-aid highway funds to convert existing signs or purchase new signs with metric units. The Executive Director of the US Federal Highway Administration, Jeffrey Paniati, wrote in a 2008 memo: "Section 205 of the National Highway System Designation Act of 1995 prohibited us from requiring any State DOT to use the metric system during project development activities. Although the State DOT's had the option of using metric measurements or dual units, all of them abandoned metric measurements and reverted to sole use of inch-pound values." 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 though world records are catalogued, the one kilometre event remains a minority event; the world records for various sporting disciplines are: Conversion of units, for comparison with other units of length Cubic metre Metric prefix Mileage Odometer Orders of magnitude Square kilometre Media related to Distance indicators at Wikimedia Commons
Orders of magnitude (area)
This page is a progressive and labelled list of the SI area orders of magnitude, with certain examples appended to some list objects. Orders of magnitude
International System of Units
The International System of Units is the modern form of the metric system, is the most used system of measurement. It comprises a coherent system of units of measurement built on seven base units, which are the ampere, second, kilogram, mole, 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 specifies names for 22 derived units, such as lumen and watt, for other common physical quantities. The base units are derived from invariant constants of nature, such as the speed of light in vacuum and the triple point of water, which can be observed and measured with great accuracy, one physical artefact; the artefact is the international prototype kilogram, certified in 1889, consisting of a cylinder of platinum-iridium, which nominally has the same mass as one litre of water at the freezing point. Its stability has been a matter of significant concern, culminating in a revision of the definition of the base units in terms of constants of nature, scheduled to be put into effect on 20 May 2019.
Derived units may be defined in terms of other derived units. They are adopted to facilitate measurement of diverse quantities; the SI is intended to be an evolving system. The most recent derived unit, the katal, was defined in 1999; the reliability of the SI depends not only on the precise measurement of standards for the base units in terms of various physical constants of nature, but on precise definition of those constants. The set of underlying constants is modified as more stable constants are found, or may be more measured. For example, in 1983 the metre was redefined as the distance that light propagates in vacuum in a given fraction of a second, thus making the value of the speed of light in terms of the defined units exact; the motivation for the development of the SI was the diversity of units that had sprung up within the centimetre–gram–second systems and the lack of coordination between the various disciplines that used them. The General Conference on Weights and Measures, established by the Metre Convention of 1875, brought together many international organisations to establish the definitions and standards of a new system and standardise the rules for writing and presenting measurements.
The system was published in 1960 as a result of an initiative that began in 1948. It is based on the metre–kilogram–second system of units rather than any variant of the CGS. Since the SI has been adopted by all countries except the United States and Myanmar; the International System of Units consists of a set of base units, derived units, a set of decimal-based multipliers that are used as prefixes. The units, excluding prefixed units, form a coherent system of units, based on a system of quantities in such a way that the equations between the numerical values expressed in coherent units have the same form, including numerical factors, as the corresponding equations between the quantities. For example, 1 N = 1 kg × 1 m/s2 says that one newton is the force required to accelerate a mass of one kilogram at one metre per second squared, as related through the principle of coherence to the equation relating the corresponding quantities: F = m × a. Derived units apply to derived quantities, which may by definition be expressed in terms of base quantities, thus are not independent.
Other useful derived quantities can be specified in terms of the SI base and derived units that have no named units in the SI system, such as acceleration, defined in SI units as m/s2. The SI base units are the building blocks of the system and all the other units are derived from them; when Maxwell first introduced the concept of a coherent system, he identified three quantities that could be used as base units: mass and time. Giorgi identified the need for an electrical base unit, for which the unit of electric current was chosen for SI. Another three base units were added later; the early metric systems defined a unit of weight as a base unit, while the SI defines an analogous unit of mass. In everyday use, these are interchangeable, but in scientific contexts the difference matters. Mass the inertial mass, represents a quantity of matter, it relates the acceleration of a body to the applied force via Newton's law, F = m × a: force equals mass times acceleration. A force of 1 N applied to a mass of 1 kg will accelerate it at 1 m/s2.
This is true whether the object is floating in space or in a gravity field e.g. at the Earth's surface. Weight is the force exerted on a body by a gravitational field, hence its weight depends on the strength of the gravitational field. Weight of a 1 kg mass at the Earth's surface is m × g. Since the acceleration due to gravity is local and varies by location and altitude on the Earth, weight is unsuitable for precision
Hectare
The hectare is an SI accepted metric system unit of area equal to a square with 100-metre sides, or 10,000 m2, is used in the measurement of land. There are 100 hectares in one square kilometre. 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, remains as a non-SI unit accepted for use with the SI units, mentioned in Section 4.1 of the SI Brochure as a unit whose use is "expected to continue indefinitely". The name was coined from the Latin ārea; the metric system of measurement was first given a legal basis in 1795 by the French Revolutionary government. The law of 18 Germinal, Year III defined five units of measure: The metre for length The are for area The stère for volume of stacked firewood The litre for volumes of liquid The gram for massIn 1960, when the metric system was updated as the International System of Units, the are did not receive international recognition.
The International Committee for Weights and Measures makes no mention of the are in the current definition of the SI, but classifies the hectare as a "Non-SI unit accepted for use with the International System of Units". In 1972, the European Economic Community passed directive 71/354/EEC, which catalogued the units of measure that might be used within the Community; the units that were catalogued replicated the recommendations of the CGPM, supplemented by a few other units including the are whose use was limited to the measurement of land. The names centiare, deciare and hectare are derived by adding the standard metric prefixes to the original base unit of area, the are; the centiare is one square metre. The deciare is ten square metres; the are is a unit of area, used for measuring land area. It was defined by older forms of the metric system, but is now outside the modern International System of Units, it is still used in colloquial speech to measure real estate, in particular in Indonesia, in various European countries.
In Russian and other languages of the former Soviet Union, 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 deca and are, is equal to 10 ares or 1000 square metres. It is used in Norway and in the former Ottoman areas of the Middle East and the Balkans as a measure of land area. Instead of the name "decare", the names of traditional land measures are used, redefined as one decare: Stremma in Greece Dunam, donum, or dönüm in Israel, Jordan, Lebanon and Turkey Mål is sometimes used for decare in Norway, from the old measure of about the same area; the hectare, although not a unit of SI, is the only named unit of area, accepted for use within the SI. In practice the hectare is derived from the SI, being equivalent to a square hectometre, it is used throughout the world for the measurement of large areas of land, it is the legal unit of measure in domains concerned with land ownership and management, including law, agriculture and town planning throughout the European Union.
The United Kingdom, United States, to some extent Canada use the acre instead. Some countries that underwent a general conversion from traditional measurements to metric measurements required a resurvey when units of measure in legal descriptions relating to land were converted to metric units. Others, such as South Africa, published conversion factors which were to be used "when preparing consolidation diagrams by compilation". In many countries, metrication clarified existing measures in terms of metric units; the following legacy units of area have been redefined as being equal to one hectare: Jerib in Iran Djerib in Turkey Gong Qing in Hong Kong / mainland China Manzana in Argentina Bunder in The Netherlands The most used units are in bold. One hectare is equivalent to: 1 square hectometre 15 mǔ or 0.15 qǐng 10 dunam or dönüm 10 stremmata 6.25 rai ≈ 1.008 chō ≈ 2.381 feddan Conversion of units Hecto- Hectometre Order of magnitude Official SI website: Table 6. Non-SI units accepted for use with the International System of Units
Area
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 two-dimensional surface of a three-dimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat, it is the two-dimensional analog of 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, the area of a square whose sides are one metre long. A shape with an area of three square metres would have the same area as three such squares. In mathematics, the unit square is defined to have area one, the area of any other shape or surface is a dimensionless real number. There are several well-known formulas for the areas of simple shapes such as triangles and circles.
Using these formulas, the area of any polygon can be found by dividing the polygon into triangles. For shapes with curved boundary, calculus is required to compute the area. Indeed, the problem of determining the area of plane figures was a major motivation for the historical development of calculus. For a solid shape such as a sphere, cone, or cylinder, the area of its boundary surface is called the surface area. Formulas for the surface areas of simple shapes were computed by the ancient Greeks, but computing the surface area of a more complicated shape requires multivariable calculus. 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, is a basic property of surfaces in differential geometry. In analysis, the area of a subset of the plane is defined using Lebesgue measure, though not every subset is measurable. 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. It can be proved. 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 so are S ∪ T and S ∩ T, a = a + a − a. If S and T are in M with S ⊆ T T − S is in M and a = a − a. If a set S is in M and S is congruent to T T is in M and a = a; every rectangle R is in M. If the rectangle has length h and breadth k a = hk. Let Q be a set enclosed between two step regions S and T. A step region is formed from a finite union of adjacent rectangles resting on a common base, i.e. S ⊆ Q ⊆ T. If there is a unique number c such that a ≤ c ≤ a for all such step regions S and T a = c, it can be proved that such an area function exists. Every unit of length has a corresponding unit of area, namely the area of a square with the given side length.
Thus areas can be measured in square metres, square centimetres, square millimetres, square kilometres, square feet, square yards, square miles, so forth. Algebraically, these units can be thought of as the squares of the corresponding length units; the SI unit of area is the square metre, considered an SI derived unit. Calculation of the area of a square whose length and width are 1 metre would be: 1 metre x 1 metre = 1 m2and so, a rectangle with different sides would have an area in square units that can be calculated as: 3 metres x 2 metres = 6 m2; this is equivalent to 6 million square millimetres. Other useful conversions are: 1 square kilometre = 1,000,000 square metres 1 square metre = 10,000 square centimetres = 1,000,000 square millimetres 1 square centimetre = 100 square millimetres. In non-metric units, the conversion between two square units is the square of the conversion between the corresponding length units. 1 foot = 12 inches,the relationship between square feet and square inches is 1 square foot = 144 square inches,where 144 = 122 = 12 × 12.
Similarly: 1 square yard = 9 square feet 1 square mile = 3,097,600 square yards = 27,878,400 square feetIn addition, conversion factors include: 1 square inch = 6.4516 square centimetres 1 square foot = 0.09290304 square metres 1 square yard = 0.83612736 square metres 1 square mile = 2.589988110336 square kilometres There are several other common units for area. The are was the original unit of area in the metric system, with: 1 are = 100 square metresThough the are has fallen out of use, the hectare is still used to measure land: 1 hectare = 100 ares = 10,000 square metres = 0.01 square kilometresOther uncommon metric units of area include the tetrad, the hectad, the myriad. The acre is commonly used to measure land areas, where 1 acre = 4,840 square yards = 43,560 square feet. An acre is 40% of a hectare. On the atomic scale, area is measured in units of barns, such that: 1 barn = 10−28 square meters; the barn is used in describing the cross-sectional area of interaction in nuclear physics.
In India, 20 dhurki = 1 dhur 20 dhur = 1 khatha 20 khata = 1 bigha 32 khata = 1 acre In the 5th century BCE, Hippocrates of Chios was the first to show that the area of a disk is proportional to the square of its diameter, as part of his quadrature of the lune of
CRC Handbook of Chemistry and Physics
The CRC Handbook of Chemistry and Physics is a comprehensive one-volume reference resource for science research in its 99th edition. It is sometimes nicknamed the "Rubber Bible" or the "Rubber Book", as CRC stood for "Chemical Rubber Company"; as late as the 1962–1963 edition the Handbook contained myriad information for every branch of science and engineering. Sections in that edition include: Mathematics and Physical Constants, Chemical Tables, Properties of Matter, Heat and Barometric Tables, Sound and Units, Miscellaneous. Earlier editions included sections such as "Antidotes of Poisons", "Rules for Naming Organic Compounds", "Surface Tension of Fused Salts", "Percent Composition of Anti-Freeze Solutions", "Spark-gap Voltages", "Greek Alphabet", "Musical Scales", "Pigments and Dyes", "Comparison of Tons and Pounds", "Twist Drill and Steel Wire Gauges" and "Properties of the Earth's Atmosphere at Elevations up to 160 Kilometers". Editions focus exclusively on chemistry and physics topics and eliminated much of the more "common" information.
22nd Edition – 44th Edition Section A: Mathematical Tables Section B: Properties and Physical Constants Section C: General Chemical Tables/Specific Gravity and Properties of Matter Section D: Heat and Hygrometry/Sound/Electricity and Magnetism/Light Section E: Quantities and Units/Miscellaneous Index 45th Edition – 70th Edition Section A: Mathematical Tables Section B: Elements and Inorganic Compounds Section C: Organic Compounds Section D: General Chemical Section E: General Physical Constants Section F: Miscellaneous Index 71st Edition – Current edition Section 1: Basic Constants and Conversion Factors Section 2: Symbols and Nomenclature Section 3: Physical Constants of Organic Compounds Section 4: Properties of the Elements and Inorganic Compounds Section 5: Thermochemistry and Kinetics Section 6: Fluid Properties Section 7: Biochemistry Section 8: Analytical Chemistry Section 9: Molecular Structure and Spectroscopy Section 10: Atomic and Optical Physics Section 11: Nuclear and Particle Physics Section 12: Properties of Solids Section 13: Polymer Properties Section 14: Geophysics and Acoustics Section 15: Practical Laboratory Data Section 16: Health and Safety Information Appendix A: Mathematical Tables Appendix B: CAS Registry Numbers and Molecular Formulas of Inorganic Substances Appendix B: Sources of Physical and Chemical Data IndexIn addition to an extensive line of engineering handbooks and references and textbooks across all scientific disciplines, CRC is today known as a leading publisher of books related to forensic sciences, forensic pathology and police sciences.
CORDIC PDF copy of the 8th edition, published in 1920 Handbook of Chemistry and Physics online Tables Relocated or Removed from CRC Handbook of Chemistry and Physics, 71st through 87th Editions