International System of Units

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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.

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.

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:

• General Conference on Weights and Measures (Conférence générale des poids et mesures or CGPM) - a meeting every four to six years of delegates from all member states;
• International Bureau of Weights and Measures (Bureau international des poids et mesures or BIPM) - an international metrology centre at Sèvres in France; and
• International Committee for Weights and Measures (Comité international des poids et mesures or CIPM) - an administrative committee which meets annually at the BIPM.

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^[update], 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 I_v (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 . 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]