Editing Metric system (section)

==Attributes==

===Ease of learning and use===
The metric system is intended to be easy to use and widely applicable, including units based on the natural world, decimal ratios, prefixes for multiples and sub-multiples, and a structure of base and derived units.

It is a [[coherent system]] with [[derived units]] built from base units using logical rather than empirical relationships and with multiples and submultiples of both units based on decimal factors and identified by a [[metric prefix|common set of prefixes]].<ref name=":0" />{{Rp|pages=15–18}}

===Extensibility===
The metric system is extensible since the governing body reviews, modifies and extends it needs arise. For example, the [[katal]], a derived unit for catalytic activity equivalent to one [[mole (unit)|mole]] per second (1&nbsp;mol/s), was added in 1999.<ref>{{Cite journal |last=Dybkær |first=René |date=2002-03-01 |title=The Tortuous Road to the Adoption of katal for the Expression of Catalytic Activity by the General Conference on Weights and Measures |journal=Clinical Chemistry |volume=48 |issue=3 |pages=586–590 |doi=10.1093/clinchem/48.3.586 |issn=0009-9147 |pmid=11861460|doi-access=free }}</ref>

=== Realisation ===
{{See also|Realisation (metrology)}}

The base units used in a measurement system must be [[Realisation (metrology)|realisable]]. To that end, the definition of each SI base unit is accompanied by a ''mise en pratique'' (practical realisation) that describes at least one way that the unit can be measured.<ref>{{cite web |url = http://www.bipm.org/en/si/new_si/mise-en-pratique.html |title = What is a ''mise en pratique''? |publisher = [[BIPM]] |year=2011 |access-date = 11 March 2011}}</ref> Where possible, definitions of the base units were developed so that any laboratory equipped with proper instruments would be able to realise a standard without reliance on an artefact held by another country.  In practice, such realisation is done under the auspices of a [[International Organization of Legal Metrology#Conformance Certification|mutual acceptance arrangement]].<ref>{{cite web |url=http://www.oiml.org/maa/ |title=OIML Mutual Acceptance Arrangement (MAA) |publisher=[[International Organization of Legal Metrology]] |access-date=23 April 2013 |url-status=dead |archive-url=https://web.archive.org/web/20130521131225/http://www.oiml.org/maa/ |archive-date=21 May 2013}}</ref>

[[File:Kilometre definition.svg|right|thumb|The [[metre]] was originally defined to be ''one ten millionth'' of the distance between the [[North Pole]] and the [[Equator]] through [[Paris]].<ref name="Alder">{{cite book |last=Alder |first=Ken |title=The Measure of all Things—The Seven-Year-Odyssey That Transformed the World |publisher=Abacus |year=2002 |isbn=978-0-349-11507-8 |location=London}}</ref>]]

In 1791 the commission originally defined the [[metre]] based on the size of the earth, equal to one ten-millionth of the distance from the equator to the North Pole. In the SI, the standard [[metre]] is now defined as exactly {{frac|1|{{val|299,792,458}}}} of the distance that light travels in a [[second]].<ref>{{cite web |url=https://www.bipm.org/en/committees/cg/cgpm/17-1983/resolution-1 |title=17th General Conference on Weights and Measures (1983), Resolution 1. |access-date=17 June 2023}}</ref><ref>{{Cite web|date=20 May 2019|title=Mise en pratique for the definition of the metre in the SI|url=https://www.bipm.org/documents/20126/41489670/SI-App2-metre.pdf/0e011055-9736-d293-5e56-b8b1b267fd68?version=1.8&t=1637238031486&download=false|website=BIPM |access-date=17 June 2023}}</ref> The metre can be realised by measuring the length that a light wave travels in a given time, or equivalently by measuring the wavelength of light of a known frequency.<ref>{{cite conference |last1=Lewis |first1=A. |title=1983 realisation of the metre definition |publisher=National Physical Laboratory |conference=Varenna Summer School |url=https://static.sif.it/SIF/resources/public/files/va2019/Lewis2.pdf |access-date=10 July 2023 |page=15 |date=4 July 2019}}</ref>

The [[kilogram]] was originally defined as the mass of one cubic decimetre of water at 4&nbsp;°C, standardised as the mass of a man-made artefact of platinum–iridium held in a laboratory in France, which was used until a [[2019 revision of the SI|new definition was introduced in May 2019]]. Replicas made in 1879 at the time of the artefact's fabrication and distributed to signatories of the [[Metre Convention]] serve as ''de facto'' standards of mass in those countries. Additional replicas have been fabricated since as additional countries have joined the convention.  The replicas were subject to periodic validation by comparison to the original, called the [[International Prototype of the Kilogram|IPK]]. It became apparent that either the IPK or the replicas or both were deteriorating, and are no longer comparable: they had diverged by 50&nbsp;μg since fabrication, so figuratively, the accuracy of the kilogram was no better than 5 parts in a hundred million or a relative accuracy of {{val|5|e=-8}}. The [[2019 revision of the SI|revision of the SI]] replaced the IPK with an exact definition of the [[Planck constant]] as expressed in SI units, which defines the kilogram in terms of fundamental constants.<ref>{{cite web |date=16 November 2018 |title=The Latest: Landmark Change to Kilogram Approved |url=https://apnews.com/e6991383703e4ad5a9570d97b0e57822 |access-date=17 June 2023 |website=AP News |publisher=Associated Press}}</ref><ref>{{Cite web |date=7 July 2021 |title=Mise en pratique for the definition of the kilogram in the SI |url=https://www.bipm.org/documents/20126/41489673/SI-App2-kilogram.pdf/5881b6b5-668d-5d2b-f12a-0ef8ca437176?version=1.9&t=1637237674882&download=false |access-date=17 June 2023 |website=BIPM}}</ref><ref>{{cite news |last1=Resnick |first1=Brian |title=The new kilogram just debuted. It's a massive achievement. |url=https://www.vox.com/science-and-health/2019/5/17/18627757/kilogram-redefined-world-metrology-day-explained |work=Vox |date=20 May 2019 |access-date=17 June 2023}}</ref>

=== Base and derived unit structure ===
{{Main|Base unit (measurement)}}
{{See also|SI derived unit}}
A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the subset can be expressed in terms of the others. A base unit is a unit adopted for expressing a base quantity. A derived unit is used for expressing any other quantity, and is a product of powers of base units. For example, in the modern metric system, length has the unit metre and time has the unit second, and speed has the derived unit metre per second.<ref name=":0" />{{Rp|page=15}} Density, or mass per unit volume, has the unit kilogram per cubic metre.<ref name=":0" />{{Rp|page=434}}

=== Decimal ratios ===
A significant characteristic of the metric system is its use of decimal multiples {{endash}} powers of 10. For example, a length that is significantly longer or shorter than 1 metre can be represented in units that are a power of 10 or 1000 metres. This differs from many older systems in which the ratio of different units varied. For example, 12 [[inch]]es is one [[foot (unit)|foot]], but the larger unit in the same system, the [[mile]] is not a power of 12 feet. It is 5,280 feet {{endash}} which is hard to remember for many.<ref name=":0" />{{Rp|page=17}}

In the early days, multipliers that were positive powers of ten were given Greek-derived prefixes such as  ''kilo-'' and ''mega-'', and those that were negative powers of ten were given Latin-derived prefixes such as ''centi-'' and ''milli-''. However, 1935 extensions to the prefix system did not follow this convention: the prefixes ''nano-'' and ''micro-'', for example have Greek roots.<ref name="McGreevy v2">{{cite book |title = The Basis of Measurement: Volume 2—Metrication and Current Practice |isbn = 978-0-948251-84-9 |publisher = Picton Publishing |location = Chippenham |year = 1997 |first1 = Thomas |last1 = McGreevy |editor1-first = Peter |editor1-last = Cunningham}}</ref>{{rp|222–223}} During the 19th century the prefix [[Non-SI unit prefix#Obsolete prefixes|''myria-'']], derived from the Greek word μύριοι (''mýrioi''), was used as a multiplier for {{val|10000}}.<ref>{{cite book |url=https://archive.org/details/edinburghencyclo07brew |title=The Edinburgh Encyclopædia |first1=D. |last1=Brewster |page=[https://archive.org/details/edinburghencyclo07brew/page/494 494] |year=1830 }}</ref>

When applying prefixes to derived units of area and volume that are expressed in terms of units of length squared or cubed, the square and cube operators are applied to the unit of length including the prefix, as illustrated below.<ref name=SI_prefix />
{| style="margin-left:3em !important; white-space:nowrap"
|-
|1&nbsp;mm<sup>2</sup> (square millimetre)         ||= (1&nbsp;mm)<sup>2</sup>&nbsp;||= (0.001&nbsp;m)<sup>2</sup>&nbsp;||= {{val|0.000001|u=m2}}
|-
|1&nbsp;km<sup>2</sup> ([[square kilometre]])&nbsp;||= (1&nbsp;km)<sup>2</sup>      ||= (1000&nbsp;m)<sup>2</sup>       ||= {{val|1000000|u=m2}}
|-
|1&nbsp;mm<sup>3</sup> (cubic millimetre)          ||= (1&nbsp;mm)<sup>3</sup>      ||= (0.001&nbsp;m)<sup>3</sup>      ||= {{val|0.000000001|u=m3}}
|-
|1&nbsp;km<sup>3</sup> (cubic kilometre)           ||= (1&nbsp;km)<sup>3</sup>      ||= (1000&nbsp;m)<sup>3</sup>       ||= {{val|1000000000|u=m3}}
|}

For the most part, the metric prefixes are used uniformly for SI base, derived and accepted units. A notable exception is that for a large measure of seconds, the non-SI units of [[minute]], [[hour]] and [[day]] are customary instead. Units of duration longer than a day are problematic since both month and year have varying number of days. Sub-second measures are often indicated via submultiple prefixes. For example, [[millisecond]].<ref name=SI_prefix />

=== Coherence ===
{{Main|Coherence (units of measurement)}}
[[File:James Clerk Maxwell.jpg|thumb|upright|[[James Clerk Maxwell]] played a major role in developing the concept of a coherent CGS system and in extending the metric system to include electrical units.]]
Each variant of the metric system has a degree of coherence—the derived units are directly related to the base units without the need for intermediate conversion factors.<ref>{{citation
| author = Working Group 2 of the Joint Committee for Guides in Metrology (JCGM/WG 2).
| publisher = [[International Bureau of Weights and Measures]] (BIPM) on behalf of the Joint Committee for Guides in Metrology
| year = 2008
| url = http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2008.pdf
| title = International vocabulary of metrology – Basic and general concepts and associated terms (VIM)
| edition = 3rd
| at = 1.12
|access-date = 12 April 2012}}</ref> For example, in a coherent system the units of [[force]], [[energy]], and [[Power (physics)|power]] are chosen so that the equations
{| style="margin-left:3em !important"
|-
| ''force''  || = || ''mass''  || × || ''acceleration''
|-
| ''energy'' || = || ''force'' || × || ''distance''
|-
| ''energy'' || = || ''power'' || × || ''time''
|}
hold without the introduction of unit conversion factors. Once a set of coherent units has been defined, other relationships in physics that use this set of units will automatically be true. Therefore, [[Albert Einstein|Einstein]]'s [[Mass–energy equivalence|mass–energy equation]], {{nowrap|1=''E'' = ''mc''{{i sup|2}}}}, does not require extraneous constants when expressed in coherent units.<ref>{{cite web
 |url=http://www.unc.edu/~mgood/research/RestEnergy.pdf
 |title=Some Derivations of ''E'' = ''mc''<sup>2</sup>
 |first1=Michael
 |last1=Good
 |access-date=18 March 2011
 |url-status=dead
 |archive-url=https://web.archive.org/web/20111107023429/https://www.unc.edu/~mgood/research/RestEnergy.pdf
 |archive-date=7 November 2011
}}</ref>

The [[centimetre–gram–second system of units|CGS system]] had two units of energy, the [[erg]] that was related to [[mechanics]] and the [[calorie]] that was related to [[thermal energy]]; so only one of them (the erg) could bear a coherent relationship to the base units. Coherence was a design aim of SI, which resulted in only one unit of energy being defined – the [[joule]].<ref name=SI_units>{{SIbrochure8th|pages = 111–120}}</ref>

=== Rationalisation ===
Maxwell's equations of electromagnetism contained a factor of <math>1/(4\pi)</math> relating to [[steradian]]s, representative of the fact that electric charges and magnetic fields may be considered to emanate from a point and propagate equally in all directions, i.e. spherically. This factor made equations more awkward than necessary, and so [[Oliver Heaviside]] suggested adjusting the system of units to remove it.<ref name=":1" />