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| − | The '''International System of Units''' (abbreviated '''SI''' from the [[French language|French]] phrase, ''Système International d'Unités'') is the most widely used [[system of units]]. It is the most common system for everyday [[commerce]] in the world, and is almost universally used in the realm of [[science]].
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| − | In [[1960]], SI was selected as a specific subset of the existing [[Metre]]-[[Kilogram]]-[[Second]] systems of units (MKS), rather than the older [[Centimetre gram second system of units|Centimetre-Gram-Second]] system (CGS). Various new units were added with the introduction of the SI and at later times. SI is sometimes referred to as the '''[[metric system]]''', especially [[Metric system in the United States|in the United States]], whose population has not widely adopted it, and in the [[United Kingdom]], where conversion is only partial. SI is a specific canon of measurements derived and extended from the ''Metric system''; however, not all metric units of measurement are accepted as SI units.
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| − | ==History==
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| − | The [[metric system]] was officially adopted in [[France]] after the [[French Revolution]]. During the [[Metric system#History|history of the metric system]] a number of variations have evolved and their use spread around the world replacing many [[Historical weights and measures|traditional measurement systems]].
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| − | By the end of [[World War II]] a number of different systems of measurement were still in use throughout the world. Some of these systems were metric system variations whilst others were based on the [[Imperial unit|Imperial]] and [[US customary units|American]] systems. It was recognised that additional steps were needed to promote a worldwide measurement system. As a result the 9th [[General Conference on Weights and Measures]] (CGPM), in [[1948]], asked the [[International Committee for Weights and Measures]] (CIPM) to conduct an international study of the measurement needs of the scientific, technical, and educational communities.
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| − | Based on the findings of this study, the 10th CGPM in [[1954]] decided that an international system should be derived from six base units to provide for the measurement of temperature and optical radiation in addition to mechanical and electromagnetic quantities. The six base units recommended were the [[metre]], [[kilogram]], [[second]], [[ampere]], [[Kelvin]] degree (later renamed the kelvin), and the [[candela]]. In [[1960]], the 11th CGPM named the system the ''International System of Units'', abbreviated SI from the French name: ''Le Système International d'Unités''. The seventh base unit, the [[mole]], was added in [[1970]] by the 14th CGPM.
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| − | The International System is now either obligatory or permissible throughout the world. It is administered by the [[standards organisation]]: the [[Bureau International des Poids et Mesures]] (International Bureau of Weights and Measures).
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| − | ===Length===
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| − | The most important unit is that of length: one [[metre]] was originally defined to be equal to 1/10 000 000<sup>th</sup> of the distance from the [[geographical pole|pole]] to the [[equator]] along the [[meridian (geography)|meridian]] through [[Paris]]. (Prior discussions had often suggested the length of a [[seconds pendulum]] in some standard gravity, which would have been only slightly shorter, and perhaps easier to determine.) This is approximately 10% longer than one [[yard]]. Later on, a [[platinum]] rod with a rigid, X-shaped cross section was produced to serve as the easy-to-check standard for one metre's length. Due to the difficulty of actually measuring the length of a meridian quadrant in the [[18th century]], the first platinum prototype was short by 0.2 millimetres. More recently, the metre was redefined as a certain multiple of a specific radiation wavelength, and currently it is defined as the distance travelled by light in a vacuum in a specific period of time. Attempts to relate an integer multiple of the metre to any meridian have been abandoned.
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| − | ===Mass===
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| − | The original base unit of mass in the metric system was the [[gram]], chosen to match the mass of one cubic centimetre of water. For practical reasons, the reference standard that was deposited at the ''Archives de la république'' on [[June 22]], [[1799]] was a kilogram (a cylinder of [[platinum]]). One kilogram is about 2.2 [[pound]]s. In [[1889]], the first [[General Conference on Weights and Measures]] (CGPM) sanctioned a replacement prototype, a cylinder of a 90% platinum, 10% [[iridium]] alloy; this has served as the standard ever since, and is stored in a Paris vault. The kilogram became the base unit in [[1901]].
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| − | Also in 1901, a kilogram of distilled pure water at its densest (+3.98 degrees [[Celsius]]) under a standard atmosphere of pressure was used to define the [[litre]], a more convenient unit than the very large cubic metre. Because this litre turned out to be different from the cubic decimetre by about 28 millionths, this definition was abandoned in [[1964]] in favour of the cubic decimetre.
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| − | The kilogram is the only base unit not to have been redefined in terms of an unchanging natural phenomenon. Such a definition, said to be in terms of an ''artefact'' (the cylinder in Paris), is particularly inconvenient, because, in principle, it can be used only by travelling to Paris and, with permission, comparing one's own candidate standard to the reference one. For this reason, as well as the effort required to protect the standard from absorption or dispersion of gases and vapours, at a meeting of the [[Royal Society]] in [[London]] on [[15 February]], [[2005]], scientists called for the mass of the <i>standard kilogramme</i> in Paris to be replaced by a standard based on "an invariable property of nature"; but no decision on redefinition can be taken before [[2007]].
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| − | ===Temperature===
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| − | The unit of temperature became the centigrade or inverted Celsius grade, which means the [[mercury-in-glass thermometer|mercury scale]] is divided into 100 equal-length parts between the water-ice mixture at 0 °C and the boiling point of pure, distilled water at 100 °C (under a standard atmosphere). This is the metric unit of temperature in everyday use. A hundred years later, the discovery of [[absolute zero]] prompted the establishment of a new temperature scale, the [[kelvin|Kelvin Scale]] which relocates the zero point at absolute zero, with the difference between freezing and boiling water close to 100 [[kelvin|K]].
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| − | ===Time===
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| − | The metric unit of time became the second, originally defined as 1/86 400<sup>th</sup> of a [[mean solar day]]. The formal definition of the second has been changed several times as more accurate definitions became possible, based first on astronomic observations, then the [[tuning fork clock]], [[quartz clock]], and today the [[caesium]] [[atomic clock]].
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| − | ==Cultural issues==
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| − | The swift worldwide adoption of the metric system as a tool of economy and everyday commerce was based mainly on the lack of customary systems in many countries to adequately describe some concepts, or as a result of an attempt to standardize the many regional variations in the customary system. International factors also affected the adoption of the metric system, as many countries increased their trade. Scientifically, it provides ease when dealing with very large and small quantities because it lines up so well with our decimal [[numeral system]].
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| − | Cultural differences can be represented in the local everyday uses of metric units. For example, bread is sold in one-half, one or two kilogram sizes in many countries, but you buy them by multiples of one hundred grams in the former [[USSR]]. In some countries, the informal ''cup'' measurement has become 250 mL, and prices for items are sometimes given per 100 g rather than per kilogram. A profound cultural difference between physicists and engineers, especially radio engineers, existed prior to the adoption of the MKS system and hence its descendent, SI. Engineers work with [[volts]], [[amperes]], [[ohms]], [[farads]], and [[coulombs]], which are of great practical utility, while the CGS units, which are fine for theoretical physics can be inconvenient for electrical engineering usage and are largely unfamiliar to householders using appliances rated in volts and watts.
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| − | Non-scientific people should not be put off by the fine-tuning that has happened to the metric base units over the past 200 years, as experts have tried frequently to refine the metric system to fit the best scientific research (e.g. CGS to MKS to SI system changes or the invention of the Kelvin scale). These changes do not affect the everyday use of metric units. The presence of these adjustments has been one reason advocates of the [[U.S. customary units]] had used against metrication; these customary units, however, are nowadays defined in terms of SI units, thus any difference in the definition of the SI units results in a difference of the definition of the customary units.
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| − | == Basis ==
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| − | SI consists of seven [[SI base unit|base units]] and several [[SI derived unit|derived units]], together with a set of [[SI prefix|prefix]]es.
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| − | The seven [[SI base unit]]s are the [[kilogram]], [[metre]], [[second]], [[ampere]], [[kelvin]], [[mole (unit)|mole]], and [[candela]].
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| − | SI also defines a number of [[SI prefix]]es to be used with the units: these combine with any unit name to give subdivisions and multiples. For example, the prefix ''kilo'' denotes a multiple of a thousand, so the ''kilo''metre is 1000 metres, the ''kilo''gram 1000 grams, and so on. The prefixes are never combined; a millionth of a kilogram is a ''milligram'', and not a 'microkilogram'.
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| − | == SI writing style ==
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| − | *Symbols are written in [[lower case]], except for symbols derived from the name of a person. For example, the unit of pressure is named after [[Blaise Pascal]], so its symbol is written "Pa" whereas the [[unit]] itself is written "[[pascal]]". The one exception is the [[litre]], whose original abbreviation "l" is dangerously similar to "1". The [[National Institute of Standards and Technology|NIST]] recommends that "L" be used instead, a usage which is common in the U.S., Canada and Australia, and has been accepted as an alternative by the CGPM. The cursive "ℓ" is occasionally seen, especially in [[Japan]], but this is not currently recommended by any standards body.<!--there are lots of standards organizations and I'm pretty sure at least some of them did recommend this in the past; I think South Africa was also big on this—> For more information, see [[Litre#Symbol|Litre]].
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| − | *Symbols are written in singular form: i.e. "25 kg", not "25 kgs". Pluralization would be language dependent; "s" plurals (as in French and English) are particularly undesirable since "s" is the symbol of the [[second]].
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| − | *Symbols do not have an appended period (.).
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| − | *It is preferable to write symbols in upright Roman type (m for metres, L for litres), so as to differentiate from the [[italic type]] used for mathematical variables (''m'' for mass, ''l'' for length).
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| − | *A space should separate the number and the symbol, e.g. "2.21 kg", "7.3×10<sup>2</sup> m<sup>2</sup>", "22 °C" [http://physics.nist.gov/Pubs/SP811/sec07.html]. Exceptions are the symbols for plane angular degrees, minutes and seconds (°, ′ and ″), which are placed immediately after the number with no intervening space.
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| − | *Spaces should be used to group decimal digits in threes, e.g. 1 000 000 or 342 142 (in contrast to the commas or dots used in other systems, e.g. 1,000,000 or 1.000.000).
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| − | *The 10th resolution of [[General Conference on Weights and Measures|CGPM]] in 2003 declared that "the symbol for the decimal marker shall be either the [[full stop|point]] on the line or the [[comma]] on the line". In practice, the full stop is used in English, and the comma in most other European languages.
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| − | *Symbols for derived units formed from multiple units by multiplication are joined with a space or centre dot (·), e.g. N m or N·m.
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| − | *Symbols formed by division of two units are joined with a [[slash (punctuation)|solidus]] (/), or given as a negative [[exponent]]. For example, the "metre per second" can be written "m/s", "m s<sup>-1</sup>", "m·s<sup>-1</sup>" or <math>\frac{\mbox{m}}{\mbox{s}}</math>. A solidus should not be used if the result is ambiguous, i.e. "kg·m<sup>-1</sup>·s<sup>-2</sup>" is preferable to "kg/m/s<sup>2</sup>".
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| − | With a few exceptions (such as draught beer sales in the United Kingdom) the system is legally being used in every country in the world and many countries do not maintain definitions of other units. Those countries that still give recognition to non-SI units (e.g. the [[United States|US]] and [[United Kingdom|UK]]) have defined many of the modern [[conversion of units|units in terms of SI units]]; for example, the common [[yard]] is defined to be exactly 0.9144 metres. In the US, survey distances are also defined in terms of metric units, but differently: 1 survey yard = 3600/3937 m. They have, however, not been redefined due to the accumulation of error it would entail and the survey foot and survey mile remain as separate units. (This was not a problem for the United Kingdom, as the [[Ordnance Survey]] has been metric since before [[World War II]].) (See [[weights and measures]] for a history of the development of units of measurement.)
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| − | == Units ==
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| − | === Base units ===
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| − | The following are the fundamental units from which all others are derived, they are dimensionally independent. The definitions stated below are widely accepted.
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| − | {{SI_base_units}}
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| − | === Dimensionless derived units ===
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| − | The following SI units are actually dimensionless ratios, formed by dividing two identical SI units. They are therefore considered by the [[International Bureau of Weights and Measures | BIPM]] to be derived. Formally, their SI unit is simply the number 1, but they are given these special names, for use whenever the lack of a unit might be confusing.
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| − | {{SI_dimensionless_units}}
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| − | === Derived units with special names ===
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| − | Base units can be put together to derive units of measurement for other quantities. Some have been given names.
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| − | {{SI_special_units}}
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| − | === Non-SI units accepted for use with SI===
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| − | The following units are not SI units but are "accepted for use with the International System."
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| − | {{SI_acceptable_units}}
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| − | === SI prefixes===
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| − | The following SI prefixes can be used to prefix any of the above units to produce a multiple or submultiple of the original unit. This includes the degree Celsius (e.g. "1.2 m°C"); however, to
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| − | avoid confusion, prefixes are ''not'' used with the time-related unit symbols min (minute), h (hour), d (day). They are not recommended for use with the angle-related symbols ° (degree), ' (minute of arc), and " (second of arc) [http://physics.nist.gov/Pubs/SP811/sec06.html], but for astronomical usage, they are sometimes used with seconds of arc.
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| − | {{SI prefixes}}
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| − | === Obsolete metric prefixes===
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| − | The following metric prefixes are no longer in use: myria-, myrio-, and any double prefixes such as those formerly used in micromicrofarads, hectokilometres, millimicrons.
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| − | ''See:'' [[Obsolete metric prefixes]]
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| − | == Spelling variations ==
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| − | Several nations, notably the [[United States]], typically use the spellings 'meter' and 'liter' instead of 'metre' and 'litre'. This is in keeping with standard [[American English]] spelling (for example, Americans also use 'center' rather than 'centre,' using the latter only rarely for its stylistic implications; see also [[American and British English differences]]). In addition, the official US spelling for the [[SI prefix]] 'deca' is 'deka'.
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| − | The US government has approved these spellings for official use. In scientific contexts only the symbols are used; since these are universally the same, the differences do not arise in practice in scientific use.
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| − | The unit 'gram' is also sometimes spelled 'gramme' in English-speaking countries other than the United States, though that is an older spelling and use is declining.
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| − | == See also ==
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| − | *[[Units of measurement]]
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| − | *[[Weights and measures]]
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| − | *[[Mesures usuelles]]
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| − | *[[Metrified English unit]]
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| − | *Other measurement systems:
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| − | **[[Imperial unit|Imperial units]]
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| − | **[[U.S. customary units]]
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| − | **[[Metre-tonne-second system of units]]
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| − | **[[Chinese unit|Chinese system of units]]
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| − | **[[Planck units]]
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| − | **[[Atomic units]]
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| − | **[[Geometrized unit system|Geometrized units]]
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| − | **[[Historical weights and measures]]
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| − | *[[CODATA]]
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| − | *[[Metrication]]
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| − | *[[Metric system in the United States]]
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| − | *[[Metrology]]
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| − | *[[UTC]] (Coordinated Universal Time)
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| − | *[[Binary prefix|Binary Prefixes]] - used to quantify large amounts of computer [[data]]
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| − | *[[Orders of magnitude]]
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| − | *[[ISO 31]]
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| − | == External links ==
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| − | ''Official''
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| − | *[http://www.bipm.fr/en/si/ BIPM (SI maintenance agency)] (home page)
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| − | *[http://www.bipm.org/en/si/si_brochure/ BIPM brochure] (SI reference)
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| − | *[http://www.iso.ch/iso/en/CatalogueDetailPage.CatalogueDetail?CSNUMBER=5448&ICS1=1 ISO 1000:1992 ''SI units and recommendations for the use of their multiples and of certain other units''], with its price tag of 99 [[Swiss franc]]s for a 22 page, coverless pamphlet showing why the public is sometimes a little slow to pick up on their recommendations.
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| − | ''Information''
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| − | * [http://physics.nist.gov/cuu/Units/index.html US NIST reference on SI]
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| − | ** [http://ts.nist.gov/ts/htdocs/200/202/pub814.htm#chart chart]
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| − | * [http://www.aticourses.com/international_system_units.htm SI - Its history and use in science and industry]
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| − | * [http://www.unc.edu/~rowlett/units/ A Dictionary of Units of Measurement]
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| − | * [http://www.unics.uni-hannover.de/ntr/russisch/si-einheiten.html5 Cyrillic transcription of SI symbols]
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| − | * Judson, Lewis B., ''Weights and Measures Standards of the United States: A brief history'', [[NIST|NBS]] Special Publication 447, orig. iss. October 1963, updated March 1976 ([http://ts.nist.gov/ts/htdocs/200/202/SP%20447.pdf 46 page PDF file])
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| − | * [http://www.france-property-and-information.com/metric_conversion_table.htm Metric system and conversion tables (courtesy French property advice)]
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| − | * [http://www.metre.info metre-info - an encyclopaedia of all metric units]
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| − | '' Pro-metric pressure groups
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| − | *[http://www.ukma.org.uk/ The UK Metric Association]
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| − | *[http://www.metric.org/ The US Metric Association]
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| − | ==Further reading==
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| − | *I. Mills, Tomislav Cvitas, Klaus Homann, Nikola Kallay, IUPAC: ''Quantities, Units and Symbols in Physical Chemistry'', 2nd ed., Blackwell Science Inc 1993, ISBN 0632035838.
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| − | [[Category:Physical sciences]]
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