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# International System of Units

The International System of Units (abbreviated SI from the French Le Système international d'unités) is the modern form of the metric system. It is the world's most widely used system of units, both in everyday commerce and in science.

The older metric system included several groups of units. The SI was developed in 1960 from the old metre-kilogram-second (mks) system, rather than the centimetre-gram-second (cgs) system, which, in turn, had a few variants.

The SI introduced several newly named units. The SI is not static — units are created and definitions are modified through international agreement among many nations as the technology of measurement progresses.

The system is nearly universally employed, and most countries do not even maintain official definitions of any other units. A notable exception is the United States, which still uses many old units in addition to SI. In the United Kingdom, conversion to metric units is government policy, but the transition is not yet complete. Those countries that still recognise non-SI units (e.g. the US and UK) have redefined their traditional non-SI units in terms of SI units.

## History

The metric system was conceived by a group of scientists (among them, Antoine-Laurent Lavoisier, who is known as the "father of modern chemistry") which had been commissioned by King Louis XVI of France to create a unified and rational system of measures. After the French Revolution, the system was adopted by the new government.[1] On August 1, 1793, the National Convention adopted the new decimal "metre" with a provisional length as well as the other decimal units with preliminary definitions and terms. On April 7, 1795 (Loi du 18 germinal, an III) the terms gramme and kilogramme replaced the former terms "gravet" (correctly "milligrave") and "grave". On December 10, 1799 (a month after Napoleon's coup d'etat), the metric system was definitively adopted in France.

The history of the metric system has seen a number of variations, whose use has spread around the world, to replace many traditional measurement systems. At 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, while others were based on the Imperial and American systems. It was recognized 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.

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, degree Kelvin (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 1971 by the 14th CGPM.

### Future development

The ISO standard ISO 31 contains recommendations for the use of the International System of Units; for applications in electrical applications additionally the IEC standard IEC 60027 has to be taken into account. As of 2008 work is proceeding[citation needed] to integrate both standards into a joint standard ISO/IEC 80000 to be referred as International System of Quantities (ISQ).

## Units

Main articles: SI base unit, SI derived unit, and SI prefix

The international system of units consists of a set of units together with a set of prefixes. The units of SI can be divided into two subsets. There are seven base units. Each of these base units are nominally dimensionally independent. From these seven base units several other units are derived. In addition to the SI units there are also a set of non-SI units accepted for use with SI.

Table 1 - SI base units[2]
Name Symbol Quantity
metre m length
kilogram kg mass
second s time
ampere A electric current
kelvin K thermodynamic temperature
mole mol amount of substance
candela cd luminous intensity

A prefix may be added to units to produce a multiple of the original unit. All multiples are integer powers of ten. For example, kilo- denotes a multiple of a thousand and milli- denotes a multiple of a thousandth hence there are one thousand millimetres to the metre and one thousand metres to the kilometre. The prefixes are never combined: a millionth of a kilogram is a milligram not a microkilogram.

Table 2 - SI Prefixes
Name yotta- zetta- exa- peta- tera- giga- mega- kilo- hecto- deca-
Symbol Y Z E P T G M k h da
Factor 1024 1021 1018 1015 1012 109 106 103 102 101
Name deci- centi- milli- micro- nano- pico- femto- atto- zepto- yocto-
Symbol d c m µ n p f a z y
Factor 10-1 10-2 10-3 10-6 10-9 10-12 10-15 10-18 10-21 10-24

## SI writing style

• Symbols do not have an appended period/full stop (.) unless at the end of a sentence.
• Symbols are written 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).
• Symbols for units 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 symbol "l" is unsuitably similar to the numeral "1" or the uppercase letter "i" (depending on the typeface used), at least in many English-speaking countries. The American National Institute of Standards and Technology recommends that "L" be used instead, a usage which is common in the US, Canada, Australia, and New Zealand (but not elsewhere). This has been accepted as an alternative by the CGPM since 1979. The cursive $\ell$ is occasionally seen, especially in Japan and Greece, but this is not currently recommended by any standards body. For more information, see Litre.
• The SI rule for pluralising units is that symbols of units are not pluralised[3], for example "25 kg" (not "25 kgs").
• The American National Institute of Standards and Technology has defined guidelines for using the SI units in its own publications and for other users of the SI[4]. These guidelines give guidance on pluralizing unit names: the plural is formed by using normal English grammar rules, for example, "henries" is the plural of "henry". The units lux, hertz, and siemens are exceptions from this rule: they remain the same in singular and plural. Note that this rule only applies to the full names of units, not to their symbols.
• A space separates the number and the symbol, e.g. "2.21 kg", "7.3×102 m²", "22 K" [5]. Exceptions are the symbols for plane angular degrees, minutes and seconds (°, ′ and ″), which are placed immediately after the number with no intervening space.
• Spaces may be used as a thousands separator (1 000 000) in contrast to commas or periods (1,000,000 or 1.000.000) in order to reduce confusion resulting from the variation between these forms in different countries. In print, the space used for this purpose is typically narrower than that between words.
• The 10th resolution of CGPM in 2003 declared that "the symbol for the decimal marker shall be either the point on the line or the comma on the line". In practice, the decimal point is used in English, and the comma in most other European languages.
• 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". [6]
• Symbols formed by division of two units are joined with a solidus (⁄), or given as a negative exponent. For example, the "metre per second" can be written "m/s", "m s−1", "m·s−1" or $\textstyle\frac{\mathrm{m}}{\mathrm{s}}.$ A solidus should not be used if the result is ambiguous, i.e. "kg·m−1·s−2" is preferable to "kg/m·s²". Many computer users will type the / character provided on American computer keyboards, which in turn produces the Unicode character U+002F, which is named solidus but is distinct from the Unicode solidus character, U+2044.
• In Chinese, Japanese, and Korean language computing (CJK), some of the commonly used units, prefix-unit combinations, or unit-exponent combinations have been allocated predefined single characters taking up a full square. Unicode includes these in its CJK Compatibility and Letterlike Symbols subranges for back compatibility, without necessarily recommending future usage.
• When writing dimensionless quantities, the terms 'ppb' (parts per billion) and 'ppt' (parts per trillion) are recognised as language-dependent terms since the value of billion and trillion can vary from language to language. SI therefore recommends avoiding these terms [1]. However, no alternative is suggested by BIPM.

### Spelling variations

• Several nations typically use the spellings meter and liter instead of metre and litre in keeping with standard American English spelling, which also corresponds to the official spelling used in several other languages, such as German, Dutch, Swedish, etc. In addition, the official US spelling for the SI prefix "deca" is deka.[7]
• In some English-speaking countries, the unit "ampere" is often shortened to amp (singular) or amps (plural).

## Conversion factors

The relationship between the units used in different systems is determined by convention or from the basic definition of the units. Conversion of units from one system to another is accomplished by use of a conversion factor. There are several compilations of conversion factors; see, for example Appendix B of NIST SP 811.[4]

## Length, mass, and temperature convergence

Specific gravity is commonly expressed in SI units or in reference to water. Since a cube with dimensions of 10 cm x 10 cm x 10 cm has volume of 1000 cm3 (often referred to as 1000 cc), which is 1 L, and when filled with water has a mass of 1 kg, water has an approximate specific gravity of 1 g/cm3 and will freeze at 0 degrees Celsius.

## Cultural issues

The worldwide adoption of the metric system as a tool of economy and everyday commerce was based to some extent on the lack of customary systems in many countries to adequately describe some concepts, or as a result of an attempt to standardise 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 simplifies dealing with very large and small quantities since it lines up so well with the decimal numeral system.

Many units in everyday and scientific use are not derived from the seven SI base units (metre, kilogram, second, ampere, kelvin, mole, and candela) combined with the SI prefixes. In some cases these deviations have been approved by the BIPM. [8] Some examples include:

• The many units of time — minute (min), hour (h), day (d) — in use besides the SI second, and are specifically accepted for use according to table 6. [9]
• The year is specifically not included but has a recommended conversion factor. [10]
• The Celsius temperature scale; kelvins are rarely employed in everyday use.
• Electric energy is often billed in kilowatt-hours instead of megajoules.
• The nautical mile and knot (nautical mile per hour) used to measure travel distance and speed of ships and aircraft (1 International nautical mile = 1852 m or approximately 1 minute of latitude at the equator). In addition to these, Annex 5 of the Convention on International Civil Aviation permits the "temporary use" of the foot for altitude.
• Astronomical distances measured in astronomical units, parsecs, and light-years instead of, say, petametres (a light-year is about 9.461 Pm or about 9 461 000 000 000 000 m).
• Atomic scale units used in physics and chemistry, such as the ångström, electronvolt, atomic mass unit, and barn.
• Some physicists still use the centimetre-gram-second (CGS) units, with their associated non-SI electric units.
• In some countries, the informal cup measurement has become 250 ml. Likewise, a 500 g "metric pound" is used in many countries. Liquids, especially alcoholic ones, are often sold in units whose origins are historical (e.g., beer in pints in the UK, champagne in Jeroboams in France).
• In the US, blood glucose measurements are recorded in milligrams per decilitre (mg/dL); in Canada and Europe, the standard is millimole per litre (mmol/L) or mM (millimolar).
• Blood pressure is measured in mmHg instead of Pa.

The fine-tuning which has happened to the metric base unit definitions over the past 200 years, as experts have tried periodically to find more precise and reproducible methods, does not affect the everyday use of metric units. Since most non-SI units in common use, such as the US customary units, are nowadays defined in terms of SI units, any change in the definition of the SI units results in a change of the definition of the older units, as well.

The European Union has a directive [11] banning non-SI markings after 31 December 2009 on any goods imported into the European Union. This applies to all markings on products, enclosed directions and papers, packaging, and advertisements. However, on September 11 2007, the EU announced that the United Kingdom would be excepted from this directive, and Imperial measurements (or, for that matter, any other kind of non-SI marking, such as "pixels" or "kilobytes") would still be permitted alongside with the metric system as supplementary indications. [12]

 Metrology Units of measurement History of measurement Orders of magnitude Metrication Metrication in the United States Organisations International Bureau of Weights and Measures (BIPM) Institute for Reference Materials and Measurements (IRMM) CODATA Standards and conventions SI base unit SI derived unit SI prefix Convention du Mètre ISO 31 ISO 1000 ISO/IEC 80000 Coordinated Universal Time (UTC)

## References

1. ^ The name "kilogram". Retrieved on 2006-07-25.
2. ^ Barry N. Taylor, Ed. [2001]. The International System of Units (SI). Gaithersburg, MD: National Institute of Standards and Technology, 9. Retrieved on 2007-10-30.
3. ^ Bureau International des Poids et Mesures (2006). "The International System of Units (SI)". 8th ed.. Retrieved on 2006-07-14.
4. ^ a b Taylor, B.N. (1995). "NIST Special Publication 811: Guide for the Use of the International System of Units (SI)". National Institute of Standards and Technology. Retrieved on 2006-06-09.
5. ^ Taylor, B. N.. NIST Guide to SI Units - Rules and Style Conventions. National Institute of Standards and Technology. Retrieved on 2007-04-12.
6. ^ Barry N. Taylor, Ed. [2001]. The International System of Units (SI). Washington, DC: National Institute of Standards and Technology, 30. Retrieved on 2007-10-15.
7. ^ Definitions of the SI units: The twenty SI prefixes. Retrieved on 2007-04-12.
8. ^ http://www.bipm.org/en/si/si_brochure/chapter4/table8.html
9. ^ http://www.bipm.org/en/si/si_brochure/chapter4/table6.html
10. ^ http://physics.nist.gov/Pubs/SP811/appenB9.html#TIME
11. ^ Council Directive 80/181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to units of measurement and on the repeal of Directive 71/354/EEC, as amended with Directive 89/617/EEC (which changed the cutoff date in article 3.2 to 31 December 1999) and Directive 1999/103/EC (which further changed the date to 31 December 2009). Retrieved on 2006-07-24.
12. ^ http://news.bbc.co.uk/1/hi/uk/6988521.stm

• International Union of Pure and Applied Chemistry (1993). Quantities, Units and Symbols in Physical Chemistry (2nd Edn). Oxford: Blackwell Science. ISBN 0-632-03583-8. Electronic version.
Information
• International System of Units at the Open Directory Project
• EngNet Metric Conversion Chart Online Categorized Metric Conversion Calculator
History
• LaTeX SIunits package manual gives a historical background to the SI system.
Pro-metric pressure groups
• The UK Metric Association
• The US Metric Association
• One Metre: Metric in Canada