# SI units: Wikis

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The International System of Units (abbreviated SI from the French le Système international d'unités[1]) is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. It is the world's most widely used system of measurement, both in everyday commerce and in science.[2][3]

The older metric system included several groups of units. The SI was developed in 1960 from the old metre-kilogram-second system, rather than the centimetre-gram-second system, which, in turn, had a few variants. Because the SI is not static, units are created and definitions are modified through international agreement among many nations as the technology of measurement progresses, and as the precision of measurements improves.

The system has been nearly globally adopted. Three principal exceptions are Burma (Myanmar), Liberia, and the United States. The United Kingdom has officially adopted the International System of Units but not with the intention of replacing customary measures entirely.

Three nations have not officially adopted the International System of Units as their primary or sole system of measurement: Burma, Liberia, and the United States.

## Realisation of units

It is very important to distinguish between the definition of a unit and its realisation. The definition of each base unit of the SI is carefully drawn up so that it is unique and provides a sound theoretical basis upon which the most accurate and reproducible measurements can be made. The realisation of the definition of a unit is the procedure by which the definition may be used to establish the value and associated uncertainty of a quantity of the same kind as the unit. A description of how the definitions of some important units are realised in practice is given on the BIPM website.[4]

A coherent SI derived unit can be expressed in SI base units with no numerical factor other than the number 1.[5] The coherent SI derived unit of resistance, the ohm, symbol Ω, for example, is uniquely defined by the relation Ω = m2·kg·s−3·A−2, which follows from the definition of the quantity electrical resistance. However, "any method consistent with the laws of physics could be used to realise any SI unit."[6] (p. 111).

## 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") who had been commissioned by 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.[7] On 1 August 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 7 April 1795 (Loi du 18 germinal, an III) the terms gramme and kilogramme replaced the former terms gravet (correctly milligrave) and grave. On 10 December 1799 (a month after Napoleon's coup d'état), the metric system was definitively adopted in France.

Countries by date of metrication
 by 1800      1820      1840      1860      1880      1900 1920      1940      1960      1980      unknown not adopted

The desire for international cooperation on metrology led to the signing in 1875 of the Metre Convention, a treaty which established three international organizations to oversee the keeping of metric standards:

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, whereas others were based on customary 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.

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 that were recommended are 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

ISO 31 contains recommendations for the use of the International System of Units; for electrical applications, in addition, IEC 60027 has to be taken into account. As of 2008, work is proceeding to integrate both standards into a joint standard Quantities and Units in which the quantities and equations used with SI are to be referred as the International System of Quantities (ISQ).[8]

A readable discussion of the present units and standards is found at Brian W. Petley International Union of Pure and Applied Physics I.U.P.A.P.- 39 (2004).

## Units

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 represents, at least in principle, different kinds of physical quantities. From these seven base units, several other units are derived. In addition to the SI units, there is also a set of non-SI units accepted for use with SI which includes some commonly used units such as the litre.

SI base units[9][10]
Name Unit symbol Quantity Symbol
metre m length l (a lowercase L)
kilogram kg mass m
second s time t
ampere A electric current I (a capital i)
kelvin K thermodynamic temperature T
candela cd luminous intensity Iv (a capital i with lowercase v subscript)
mole mol amount of substance n

A prefix may be added to a unit 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.

Standard prefixes for the SI units of measure
Multiples Name deca- hecto- kilo- mega- giga- tera- peta- exa- zetta- yotta-
Symbol da h k M G T P E Z Y
Factor 100 101 102 103 106 109 1012 1015 1018 1021 1024

Subdivisions Name deci- centi- milli- micro- nano- pico- femto- atto- zepto- yocto-
Symbol d c m µ n p f a z y
Factor 100 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 (.).
• Symbols are written in upright (Roman) type (m for metres, s for seconds), so as to differentiate from the italic type used for variables (m for mass, s for displacement). By consensus of international standards bodies, this rule is applied independent of the font used for surrounding text.[11]
• 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". All symbols of prefixes larger than 103 (kilo) are also uppercase.
• 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 and Australia (but not elsewhere). This has been accepted as an alternative by the CGPM since 1979. The cursive ℓ 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 is that symbols of units are not pluralised, for example "25 kg" (not "25 kgs").[11]
• The American National Institute of Standards and Technology has defined guidelines for American users of the SI.[12][13] These guidelines give guidance on pluralising unit names: the plural is formed by using normal English grammar rules, for example, "henries" is the plural of "henry".[12]:31 The units lux, hertz, and siemens are exceptions from this rule: They remain the same in singular and plural. Note that this rule applies only 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". This rule explicitly includes the percent sign (%). Exceptions are the symbols for plane angular degrees, minutes and seconds (°, ′ and ″), which are placed immediately after the number with no intervening space.[14][15]
• Spaces may be used as a thousands separator (1000000) 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 (commonly a thin space).
• Any line-break inside a number, inside a compound unit or between number and unit should be avoided, but, if necessary, the latter option should be used.
• 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-speaking countries as well as most of Asia and the comma in most continental European languages.
• Symbols for derived units (formed from multiple units by multiplication) are joined with a centre dot (·), dot (.)[16], or a non-break space, for example, "N·m", "N.m", or "N m".[17]
• 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 $\textstyle\frac{\mathrm{m}}{\mathrm{s}}$. Only one solidus should be used; e.g., "kg/(m·s2)" or "kg·m−1·s−2" are acceptable but "kg/m/s2" is ambiguous and unacceptable. Many computer users will type the / character provided on 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.[18] However, no alternative is suggested by the International Bureau of Weights and Measures (BIPM).

### Spelling variations

• The official US spellings for deca, metre, and litre are deka, meter, and liter, respectively.[19]
• In some English-speaking countries, the unit ampere is often shortened to amp (singular) or amps (plural) in informal writing as well as on many electrical appliances. Secs may sometimes be seen instead of s or seconds.

## 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.[12]

## Length, mass and temperature convergence

Density (specific mass) is commonly expressed in SI units or in reference to water. Since a cube with sides of 1 decimetre has volume of 1 cubic decimetre, which is 1 litre and, when filled with water, has a approximate mass of 1 kilogram, water has an approximate density of 1 kilogram per litre, which is equal to 1 gram per cubic centimetre and 1 tonne per cubic metre, and will freeze at approximately 0 degrees Celsius at 1 atmosphere of pressure.

Note that this is only an approximate definition of the kilogram, as the density of water can change with temperature; the actual definition is based on a specific platinum-iridium cylinder held in a vault at the BIPM in Sèvres, France.

## Cultural issues

The near-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. For use in science, 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.[20] 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.[21]
• The year is specifically not included but has a recommended conversion factor.[22]
• 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). 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 9461000000000000 m).
• Atomic scale units used in physics and chemistry, such as the ångström, electron volt, atomic mass unit and barn.
• Some physicists prefer 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 (for example, pints for beer and cider in glasses in the UK —although pint means 568 ml; champagne in Jeroboams in France).
• A metric mile of 10 km is used in Norway and Sweden. The term metric mile is also used in some English speaking countries for the 1500 m foot race.
• In the US, blood glucose measurements are recorded in milligrams per decilitre (mg/dL), which would normalise to cg/L; in Canada, Australia, New Zealand, Oceania 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 that 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 SI units,[23] any change in the definition of the SI units results in a change of the definition of the older units, as well.

One of the European Union's (EU) objectives is the creation of a single market for trade. In order to achieve this objective, the EU standardised on using SI as the legal units of measure. At the time of writing (2009) it had issued two units of measurement directives which catalogued the units of measure that might be used for, amongst other things, trade: the first was Directive 71/354/EEC[24] issued in 1971 which required member states to standardise on SI rather than use the variety of cgs and mks units then in use. The second was Directive 80/181/EEC[25][26][27][28][29] issued in 1979 which replaced the first and which gave the United Kingdom and the Republic of Ireland a number of derogations from the original directive.

The directives gave a derogation from using SI units in areas where other units of measure had either been agreed by international treaty or which were in universal use in worldwide trade. They also permitted the use of supplementary indicators alongside, but not in place of the units catalogued in the directive. In its original form, Directive 80/181/EEC had a cut-off date for the use of such indicators, but with each amendment this date was moved until, in 2009, supplementary indicators have been allowed indefinitely.

 Organisations Standards and conventions

## References

1. ^ Bureau International des Poids et Mesures
2. ^ Official BIPM definitions
3. ^ An extensive presentation of the SI units is maintained on line by NIST, including a diagram of the interrelations between the derived units based upon the SI units. Definitions of the basic units can be found on this site, as well as the CODATA report listing values for special constants such as the electric constant, the magnetic constant and the speed of light, all of which have defined values as a result of the definition of the metre and ampere.

In the International System of Units (SI) (BIPM, 2006), the definition of the meter fixes the speed of light in vacuum c0, the definition of the ampere fixes the magnetic constant (also called the permeability of vacuum) μ0, and the definition of the mole fixes the molar mass of the carbon 12 atom M(12C) to have the exact values given in the table [Table 1, p.7]. Since the electric constant (also called the permittivity of vacuum) is related to μ0 by ε0 = 1/μ0c02, it too is known exactly.

– CODATA report
4. ^ SI Practical Realization brochure
5. ^ Ambler Thompson and Barry N. Taylor, (2008), Guide for the Use of the International System of Units (SI), (Special publication 811), Gaithersburg, MD: National Institute of Standards and Technology, p. 3, footnote 2.
6. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (8th ed.), p. 111, ISBN 92-822-2213-6
7. ^ "The name "kilogram"". Retrieved 25 July 2006.
8. ^ SI Brochure
9. ^ Barry N. Taylor & Ambler Thompson Ed.. The International System of Units (SI). Gaithersburg, MD: National Institute of Standards and Technology. pp. 23. Retrieved 18 June 2008.
10. ^ Quantities Units and Symbols in Physical Chemistry, IUPAC
11. ^ a b Bureau International des Poids et Mesures (2006). The International System of Units (SI). 8th ed.. Retrieved 13 February 2008.  Chapter 5.
12. ^ a b c Ambler Thompson & Barry N. Taylor (2008). NIST Special Publication 811: Guide for the Use of the International System of Units (SI). National Institute of Standards and Technology. Retrieved 18 June 2008.
13. ^ Turner, James M. (9 May 2008). "Interpretation of the International System of Units (the Metric System of Measurement) for the United States". Federal Register (National Archives and Records Administration) 73 (96): 28432–3. FR Doc number E8-11058. Retrieved 28 October 2009.
14. ^ The International System of Units (SI) (8 ed.). International Bureau of Weights and Measures (BIPM). 2006. p. 133.
15. ^ Thompson, A.; Taylor, B. N. (July 2008). "NIST Guide to SI Units — Rules and Style Conventions". National Institute of Standards and Technology. Retrieved 29 December 2009.
16. ^ National Standard of Canada. Canadian Metric Practice Guide, CAN/CSA-Z234.1-89, 1989, item 3.8.1
17. ^ Barry N. Taylor, Ed.. The International System of Units (SI). Washington, DC: National Institute of Standards and Technology. pp. 30. Retrieved 2007-10-15.
18. ^ http://www.bipm.org/en/si/si_brochure/chapter5/5-3-7.html
19. ^ "The International System of Units". pp. iii. Retrieved 2008-05-27.
20. ^ BIPM - Table 8
21. ^ BIPM - Table 6
22. ^ NIST Guide to SI Units - Appendix B9. Conversion Factors
23. ^ Mendenhall, T. C. (1893). "Fundamental Standards of Length and Mass". Reprinted in Barbrow, Louis E. and Judson, Lewis V. (1976). Weights and measures standards of the United States: A brief history (NBS Special Publication 447). Washington D.C.: Superintendent of Documents. Viewed 23 August 2006 at http://physics.nist.gov/Pubs/SP447/ pp. 28–29.
24. ^
25. ^ The Council of the European Communities (1979-12-21). "Council Directive 80/181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC". Retrieved 2009-02-07.
26. ^ The Council of the European Communities (1984-12-20). "Council Directive 80/181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC". Retrieved 2009-02-07.
27. ^ The Council of the European Communities (1989-11-30). "Council Directive 80/181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC". Retrieved 2009-02-07.
28. ^ The Council of the European Communities (2000-02-09). "Council Directive 80/181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC". Retrieved 2009-02-07.
29. ^ The Council of the European Communities (2009-05-27). "Council Directive 80/181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC". Retrieved 2009-09-14.

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