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"SI" redirects here. For other uses, see Si (disambiguation).
For a topical guide, see Outline of the metric system.
The seven SI base units and the interdependency of their definitions

The International System of Units (abbreviated SI from French: Système international d'unités) is the modern form of the metric system. It comprises a system of units of measurement devised around seven base units and the convenience of the number ten. The SI was established in 1960,[1] based on the metre-kilogram-second system, rather than the centimetre-gram-second system, which, in turn, had several variants. The SI has been declared to be an evolving system; thus prefixes and units are created and unit definitions are modified through international agreement as the technology of measurement progresses, and as the precision of measurements improves. SI is the world's most widely used system of measurement, used in both everyday commerce and science.[2][3][4]

The system has been nearly globally adopted with Burma, Liberia and the United States not having adopted SI units as their official system of weights and measures. While only the US does not commonly use metric units outside of science, medicine, and the government,[5] the United Kingdom has officially adopted a partial metrication policy, with no intention of replacing imperial units entirely. Canada has adopted it for most purposes but imperial units, which are used in the United States, are still legally permitted and remain in common use throughout a few sectors of Canadian society, particularly in the buildings trades and railways sectors.[6][7]

History

Main article: History of the metric system

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 the Assemblée nationale and Louis XVI of France to create a unified and rational system of measures.[8]

Old boundary stone in Pontebba, marking the former border between Austria-Hungary and Italy; the myriametre (10 km), since deprecated, was in common use in Central Europe during the mid nineteenth century[9]

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, and on 22 June 1799, after Pierre Méchain and Jean-Baptiste Delambre completed their survey, the definitive standard metre was deposited in the French National Archives. On 10 December 1799 (a month after Napoleon's coup d'état), the law by which metric system was to be definitively adopted in France was passed.[10]

The desire for international cooperation on metrology led to the signing in 1875 of the Metre Convention, a treaty that established three international organisations to oversee the keeping of metric standards:[11]

The history of the metric system has seen a number of variations, and 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. After representations by the International Union of Pure and Applied Physics (IUPAP) and by the French Government, 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.[12]

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 kelvin), and 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] Error: {{Lang}}: text has italic markup (help).[13][14] The BIPM has also described SI as "the modern metric system".[15] The seventh base unit, the mole, was added in 1971 by the 14th CGPM.

SI Brochure and conversion factors

File:SI Brochure Cover.jpg
Cover of brochure The International System of Units

The CGPM have published a brochure, the 8th edition of which appeared in 2006, in which the various recommendations that make up SI have been codified.[16] This brochure leaves some scope for local interpretation, particularly in respect of language. The United States National Institute of Standards and Technology has produced a version of the CGPM document (NIST SP 811) which clarifies local interpretation in respect of English-language publications that use American English.[17]

The writing and maintenance of the CGPM brochure is carried out by one of the consultative committees of the International Committee for Weights and Measures (CIPM) - the Consultative Committee for Units (CCU). The CIPM nominates the chairman of this committee, but its membership is made up of representatives of various other international bodies rather than CIPM or CGPM nominees.[18][Note 1] This committee also provides a forum for the bodies concerned to provide input to the CIPM in respect of on-going enhancements to SI. In 2010 the CCU proposed a number of changes to the definitions of the base units used in SI.[19] The CIPM meeting of October 2010 found that the proposal was not complete,[20] and it is expected that the CGPM will consider the full proposal in 2014.

The definitions of the terms 'quantity', 'unit', 'dimension' etc that are used in the SI Brochure are those given in the International Vocabulary of Metrology, a publication produced by the Joint Committee for Guides in Metrology (JCGM), a working group consisting of eight international standards organisations under the chairmanship of the director of the BIPM.[21] The quantities and equations that define the SI units are now referred to as the International System of Quantities (ISQ), and are set out in the ISO/IEC 80000 Quantities and Units.

Appendix B of NIST SP 811, a list of conversion factor between SI and customary units, is an extension to the SI Brochure. [22]

Units and prefixes

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

The International System of Units consists of a set of units together with a set of prefixes. The units are divided into two classes—base units and derived units. There are seven base units, each representing, by convention, different kinds of physical quantities.

SI base units[23][24]
Unit name Unit
symbol 		Quantity Quantity symbol Dimension
symbol
metre m length l (a lowercase L), x, r L
kilogram [note 1] kg mass m M
second s time t T
ampere A electric current I (an uppercase i) I
kelvin K thermodynamic temperature T Θ
mole mol amount of substance n N
candela cd luminous intensity Iv (an uppercase i with lowercase non-italicized v subscript) J
Note
  1. ^ Despite the prefix "kilo-", the kilogram is the base unit of mass. The kilogram, not the gram, is used in the definitions of derived units.
    Nonetheless, units of mass are named as if the gram were the base unit.

Derived units are formed from multiplication and division of the seven base units and other derived units[25] and are unlimited in number;[26] for example, the SI derived unit of speed is metre per second, m/s. Some derived units have special names; for example, the unit of resistance, the ohm, symbol Ω, is uniquely defined by the relation Ω = m2·kg·s−3·A−2, which follows from the definition of the quantity electrical resistance. The radian and steradian, once given special status, are now considered dimensionless derived units.[25]

Named units derived from SI base units
Name Symbol Quantity Relationship with
other units 		Dimension
symbol
hertz Hz frequency 1/s T−1
radian rad angle m/m dimensionless
steradian sr solid angle m2/m2 dimensionless
newton N force, weight kg⋅m/s2 M⋅L⋅T−2
pascal Pa pressure, stress N/m2 M⋅L−1⋅T−2
joule J energy, work, heat N⋅m = C⋅V = W⋅s M⋅L2⋅T−2
watt W power, radiant flux J/s = V⋅A M⋅L2⋅T−3
coulomb C electric charge or quantity of electricity s⋅A T⋅I
volt V voltage, electrical potential difference, electromotive force W/A = J/C M⋅L2⋅T−3⋅I−1
farad F electric capacitance C/V M−1⋅L−2⋅T4⋅I2
ohm Ω electric resistance, impedance, reactance V/A M⋅L2⋅T−3⋅I−2
siemens S electrical conductance 1/Ω = A/V M−1⋅L−2⋅T3⋅I2
weber Wb magnetic flux J/A M⋅L2⋅T−2⋅I−1
tesla T magnetic field strength V⋅s/m2 = Wb/m2 = N/(A⋅m) M⋅T−2⋅I−1
henry H inductance V⋅s/A = Wb/A M⋅L2⋅T−2⋅I−2
degree Celsius °C temperature relative to 273.15 K K Θ
lumen lm luminous flux cd⋅sr J
lux lx illuminance lm/m2 L−2⋅J
becquerel Bq radioactivity (decays per unit time) 1/s T−1
gray Gy absorbed dose (of ionizing radiation) J/kg L2⋅T−2
sievert Sv equivalent dose (of ionizing radiation) J/kg L2⋅T−2
katal kat catalytic activity mol/s T−1⋅N

A prefix may be added to a unit to produce a multiple of the original unit. All multiples are integer powers of ten, and beyond a hundred(th) all are integer powers of a thousand. 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, and multiples of the kilogram are named as if the gram was the base unit. Thus a millionth of a metre is a micrometre, not a millimillimetre, and a millionth of a kilogram is a milligram, not a microkilogram.[27]

Standard prefixes for the metric units of measure (multiples)
Prefix name N/A deca hecto kilo mega giga tera peta exa zetta yotta ronna quetta
Prefix symbol da h k M G T P E Z Y R Q
Factor 100 101 102 103 106 109 1012 1015 1018 1021 1024 1027 1030
Standard prefixes for the metric units of measure (submultiples)
Prefix name N/A deci centi milli micro nano pico femto atto zepto yocto ronto quecto
Prefix symbol d c m μ n p f a z y r q
Factor 100 10−1 10−2 10−3 10−6 10−9 10−12 10−15 10−18 10−21 10−24 10−27 10−30

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 non-coherent units such as the litre.

Writing unit symbols and the values of quantities

Before 1948, the writing of metric quantities was haphazard. In 1879, the CIPM published recommendations for writing the symbols for length, area, volume, and mass, but it was outside its domain to publish recommendations for other quantities. Beginning in about 1900, physicists who had been using the symbol "μ" for "microgram", "λ" for "microlitre", and "γ" for "microgram" started to use the symbols "μm", "μg" and "μL", but it was only in 1935, a decade after the revision of the Metre Convention that the CIPM formally adopted this proposal and recommended that the symbol "μ" be used universally as a prefix for 10-6.[28]

In 1948, the ninth CGPM approved the first formal recommendation for the writing of symbols in the metric system when the basis of the rules as they are now known was laid down.[29] When, in 1960, the International System of Units was introduced, the rules that were put in place in 1948 were adapted for use with the new system. Since then the rules, apart from some minor modifications, have remained in place.

Writing the unit names

The CGPM rules state that the names of units follow the grammatical rules associated with common nouns: in English and in French they start with a lowercase letter (e.g., newton, hertz, pascal), even when the symbol for the unit begins with a capital letter. This also applies to "degrees Celsius", since "degree" is the unit. In German, however, the names of units, just like all German nouns, start with capital letters.[30] The spelling of unit names is a matter for the guardians[Note 2] of the language concerned - the official British and American spellings for certain SI units differ - British English uses the spelling deca-, metre, and litre whereas American English uses the spelling deka-, meter, and liter, respectively.[31]

Likewise, the plural form of units follow the grammar of the language concerned: in English, the normal rules of English grammar are used.[22][32] e.g. "henries" is the plural of "henry".[22]: 31  However the units lux, hertz, and siemens have irregular plurals in that they remain the same in both their singular and plural form.

In English, when unit names are combined to denote multiplication of the units concerned, they are separated with a hyphen or a space (e.g. newton-metre or newton metre). The plural is formed by converting the last unit name to the plural form (e.g. ten newton-metres).

Representation of SI units in Chinese and Japanese

Chinese expressway distances road sign in eastern Beijing. Although the primary text is in Chinese, the distances use the internationally recognised numerals and symbols.

Japanese and Chinese script use logograms rather than letters, and the rules for the writing unit names have been adapted to suit the languages.

In Japanese: Individual Chinese characters exist for some SI units, namely metre, litre, and gram, with the prefixes from kilo- (1000) to milli- (1/1000), yielding 21 (3×7) characters. These were created in Japan in the late 19th century (Meiji period) by choosing characters for the basic units – 米 "metre", 升 "litre", and 克 "gram" – and for the prefixes – 千 "kilo-, 1000", 百 "hecto-, 100", 十 "deca-, 10", 分 "deci-, 1/10", 厘 "centi-, 1/100", and 毛 "milli-, 1/1000" – and then combining them to form a single character, such as 粁 (米+千) for kilometre (in the case of no prefix, the base character alone is used). The entire metre series, for example, is 粁, 粨, 籵, 米, 粉, 糎, 粍.

In Chinese: The basic units are 米 mǐ "metre", 升 shēng "litre", 克 kè "gram", and 秒 mǐao "second". Some sample prefixes are 分 fēn "deci", 厘 lí "centi", 毫 háo "milli", and 微 wēi "micro". These are not combined into a single character, so for example centimetres are simply 厘米 límǐ.[33]

The symbols for the metric units are internationally-recognised Latin characters or, in respect of "Ω" or "μ", Greek characters.

Writing unit symbols and the values of quantities

Although the writing of unit names is language-specific, the writing of unit symbols and the values of quantities is consistent across all languages and as such the SI brochure has specific rules in respect of writing them.[34] The guideline produced by NIST[35] clarifies language-specific areas in respect of American English that were left open by the SI brochure, but is otherwise identical to the SI brochure.[32]

General rules

General rules[Note 3] for writing SI units and quantities apply to text that is either hand-written or produced using an automated process:

  • Symbols are mathematical entities, not abbreviations and as such do not have an appended period/full stop (.) unless the rules of grammar demand one for another reason such as denoting the end of a sentence.
  • A prefix is part of the unit, and its symbol is prepended to the unit symbol without a separator (e.g., "k" in "km", "M" in "MPa", "G" in "GHz"). Compound prefixes are not allowed.
  • Symbols for derived units formed by multiplication are joined with a centre dot (•) or a non-break space; e.g., N•m or N m.
  • Symbols for derived units formed by division are joined with a solidus (/), or given as a negative exponent. E.g., the "metre per second" can be written m/s, m s−1, m•s−1, or m/s. Only one solidus should be used; e.g., kg/(m•s2) and kg•m−1•s−2 are acceptable, but kg/m/s2 is ambiguous and unacceptable.
  • The first letter of symbols for units derived from the name of a person is written in upper case, otherwise they are written in lower case. For example, the unit of pressure is named after Blaise Pascal, so its symbol is written "Pa" but the symbol for mole is written "mol". Thus "T" is the symbol for teslas, a measure of magnetic field strength and "t" the symbol for tonnes, a measure of mass. Since 1979 the litre may exceptionally be written using either an upper case "L" or a lower case "l", a decision prompted by the similarity of the lower case letter "l" to the numeral "1", especially with certain type-faces or English-style handwriting. The American National Institute of Standards and Technology recommends that within the United States "L" be used rather than "l".
  • Symbols of units do not have a plural form; e.g., "25 kg", not "25 kgs".
  • Upper-case and lower-case prefixes should not be inter-changed - the quantities "1 mW" and "1 MW" represent two different quantities, the former is the typical power requirement of a hearing aid and the latter typical power requirement of a suburban train.
  • 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 and most of Asia, and the comma in most of Latin America and in continental European languages.[36]
  • Spaces should 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.
  • Any line-break inside a number, inside a compound unit, or between number and unit should be avoided. Where this is not possible, line breaks should coincide with thouands separators.
  • Since the value of "billion" and "trillion" can vary from language to language, the dimensionless terms 'ppb' (parts per billion) and 'ppt' (parts per trillion) should be avoided. However, no alternative is suggested in the SI Brochure.

Printing SI symbols

Further rules[Note 3] are specified in respect of production of text using printing presses, word processors, typewriters and the like.

  • Symbols are written in upright (Roman) type (m for metres, s for seconds), so as to differentiate from the italic type used for quantities (m for mass, s for displacement). By consensus of international standards bodies, this rule is applied independent of the font used for surrounding text.
  • The value of a quantity is written as a number followed by a space (representing a multiplication sign) and a unit symbol; e.g., "2.21 kg", "7.3×102 m2", "22 K". This rule explicitly includes the per cent sign (%). Exceptions are the symbols for plane angular degrees, minutes and seconds (°, ′ and ″), which are placed immediately after the number with no intervening space.
  • 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 Letter like Symbols subranges for back compatibility, without necessarily recommending future usage. These are summarised in Unicode symbols. The cursive ℓ, a letter-like symbol, has been used in a number of countries in addition to China and Japan as a symbol for the litre but this is not currently recommended by any standards body.
  • In print, the space used as a thousands separator (commonly called a thin space) is typically narrower than that used between words.

Realisation of units

Metrologists carefully distinguish between the definition of a unit and its realisation. The definition of each base unit of the SI is drawn up so that it is unique and provides a sound theoretical basis on 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 the practical realisation (French: Mise en pratique) of the base units are given in an electronic appendix to the SI brocure.[37]

The published mise en pratique is not the only way in which a base unit can be determined: the SI brochure states that "any method consistent with the laws of physics could be used to realise any SI unit."[38] In the current (2012) exercise to overhaul the definitions of the base units, various consultative committees of the CIPM have required that more than one mise en practique shall be developed for determining the value of each unit. In particular:

  • At least three separate experiments be carried out yielding values having a relative standard uncertainty in the determination of the kilogram of no more than 5 x 10-8 and at least one of these values should be better than 2 x 10-8. Both the Watt balance and the Avogadro project should be included in the experiments and any differences between these be reconciled.[39][40]
  • When determining the kelvin, the relative uncertainty of Boltzmann constant derived from two fundamentally different methods such as acoustic gas thermometry and dielectric constant gas thermometry be better than one part in 10-6 and that these values be corroborated by other measurements.[41]

Cultural issues

The CIA identifies three nations have not adopted the International System of Units as their official system of measurement: Myanmar (Burma), Liberia, and the United States[5]

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, the SI prefixes simplify dealing with very large and small quantities.

Many units in everyday and scientific use are not SI units. In some cases these units have been designated by the BIPM as "non-SI units accepted for use with the SI". [42] [43] Some examples include:

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 defined in SI units,[49] any change in the definition of the SI units results in a change of the definition of the older units, as well.

International trade

Main articles: Metrication in the United States and Metrication in the United Kingdom

One of the European Union's (EU) objectives is the creation of a single market for trade. To achieve this objective, the EU standardised on using SI as the legal units of measure. As of 2009, it has 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[50] 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[51][52][53][54][55] issued in 1979, which replaced the first and 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 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.

"New SI"

Main article: New SI definitions
Relations between proposed SI units definitions (in colour) and seven physical constants (in grey) with fixed numerical values in the proposed system.

When the metre was redefined in 1960, the kilogram was the only SI base unit that relied on a specific artefact. Moreover, after the 1996–1998 recalibration, a clear divergence between the various prototype kilograms was observed.

At its 23rd meeting (2007), the CGPM mandated the CIPM to investigate the use of natural constants as the basis for all units of measure rather than the artifacts that were then in use. At a meeting of the CCU held in Reading, United Kingdom in September 2010, a resolution[56] and draft changes to the SI brochure that were to be presented to the next meeting of the CIPM in October 2010 were agreed to in principle.[19] The proposals that the CCU put forward were:

The CIPM meeting of October 2010 found that "the conditions set by the General Conference at its 23rd meeting have not yet been fully met. For this reason the CIPM does not propose a revision of the SI at the present time".[57] The CIPM did however sponsor a resolution at the 24th CGPM in which the changes were agreed in principle and which were expected to be finalised at the CGPM's next meeting in 2014.[58]

See also

Organisations
Standards and conventions

Notes

  1. ^ These bodies include:
  2. ^ For example, the Académie française in the case of French or Council for German Orthography (German: Rat für deutsche Rechtschreibung) in the case of German
  3. ^ a b Except where specifically noted, these rules are common to both the SI brochure and the NIST brochure.

References

  1. ^ "International aspects of the SI". Washington, DC: National Institute of Standards and Technology. Retrieved 23 September 2012.
  2. ^ Official BIPM definitions
  3. ^ Essentials of the SI: Introduction
  4. ^ An extensive presentation on SI units is maintained on-line by NIST, including a diagram of the relations between the derived units based on the SI units. Definitions of the basic units can be found on this site, as well as the CODATA report, which lists 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 metre 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
  5. ^ a b "Appendix G : Weights and Measures". The World Factbook. Central Intelligence Agency. Retrieved 3 September 2011.
  6. ^ Weights and Measures Act
  7. ^ Weights and Measures Act, Retrieved 2012-09-18, Act current to 18 September 2012. "Canadian units (5) The Canadian units of measurement are as set out and defined in Schedule II, and the symbols and abbreviations therefor are as added pursuant to subparagraph 6(1)(b)(ii)."
  8. ^ "The name "kilogram"". Retrieved 25 July 2006.
  9. ^ Cite error: The named reference Europa1842 was invoked but never defined (see the help page).
  10. ^ Smeaton, William A. (2000). "The Foundation of the Metric System in France in the 1790s: The importan e of Etienne Lenoir's platinum measuring instruments" (PDF). Platinum Metals Rev. 44 (3). Ely, Cambridgeshire, United Kingdom: 125–134. Retrieved 10 November 2012.
  11. ^ "The Metre Convention". Bureau International des Poids et Mesures. Retrieved 1 October 2012.
  12. ^ "Resolution 6 of the 9th meeting of the CGPM (1948)". International Bureau for Weights and Measures. 1948. Retrieved 10 November 2012.
  13. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), ISBN 92-822-2213-6, archived (PDF) from the original on 4 June 2021, retrieved 16 December 2021
  14. ^ Resolution of the International Bureau of Weights and Measures establishing the International System of Units
  15. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 95, ISBN 92-822-2213-6, archived (PDF) from the original on 4 June 2021, retrieved 16 December 2021]]
  16. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), ISBN 92-822-2213-6, archived (PDF) from the original on 4 June 2021, retrieved 16 December 2021
  17. ^ Thompson, Ambler; Taylor, Barry N. (2008). Guide for the Use of the International System of Units (SI) (Special publication 811) (PDF). Gaithersburg, MD:: National Institute of Standards and Technology. {{cite book}}: Cite has empty unknown parameter: |1= (help)CS1 maint: extra punctuation (link)
  18. ^ "Criteria for membership of the CCU". Bureau International des Poids et Mesures. Retrieved 25 September 2012.
  19. ^ a b Ian Mills (29 September 2010). "Draft Chapter 2 for SI Brochure, following redefinitions of the base units" (PDF). CCU. Retrieved 1 January 2011.
  20. ^ Anon (November 2010). "BIPM Bulletin" (PDF). BIPM. Retrieved 5 January 2011.
  21. ^ "The International Vocabulary of Metrology (VIM)".
  22. ^ a b c Ambler Thompson & Barry N. Taylor (2008). "NIST Special Publication 811: Guide for the Use of the International System of Units (SI)" (PDF). National Institute of Standards and Technology. Retrieved 18 June 2008. {{cite journal}}: Cite journal requires |journal= (help)
  23. ^ Barry N. Taylor & Ambler Thompson Ed. (2008). The International System of Units (SI) (PDF). Gaithersburg, MD: National Institute of Standards and Technology. p. 23. Retrieved 18 June 2008.
  24. ^ Quantities Units and Symbols in Physical Chemistry, IUPAC
  25. ^ a b 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.
  26. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 103, ISBN 92-822-2213-6, archived (PDF) from the original on 4 June 2021, retrieved 16 December 2021
  27. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), pp. 121–122, ISBN 92-822-2213-6, archived (PDF) from the original on 4 June 2021, retrieved 16 December 2021
  28. ^ McGreevy, Thomas (1997). Cunningham, Peter (ed.). The Basis of Measurement: Volume 2 – Metrication and Current Practice. Pitcon Publishing (Chippenham) Ltd. pp. 222–224. ISBN 0 948251 84 0.
  29. ^ "Resolution 7 of the 9th meeting of the CGPM (1948): Writing and printing of unit symbols and of numbers". International Bureau for Weights and Measures (BIPM). Retrieved 6 November 2012.
  30. ^ Wörterbuch Englisch Dictionary German. Limassol: Eurobuch/Eurobooks. 1988.
  31. ^ "The International System of Units" (PDF). pp. iii. Retrieved 27 May 2008.
  32. ^ a b "Interpretation of the International System of Units (the Metric System of Measurement) for the United States" (PDF). Federal Register. 73 (96). National Archives and Records Administration: 28432–3. 9 May 2008. FR Doc number E8-11058. Retrieved 28 October 2009.
  33. ^ Frysinger, James R.; Yin, Pin; Jih, Justin; Jih, Yeeming (2010). "SI Unit and Prefix Names in Chinese". Metric Methods. Retrieved 1 November 2012.
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