Ametric prefixis aunit prefixthat precedes a basic unit of measure to indicate amultiple or submultipleof the unit. All metric prefixes used today aredecadic.Each prefix has a unique symbol that is prepended to any unit symbol. The prefixkilo-,for example, may be added togramto indicatemultiplicationby one thousand: onekilogramis equal to one thousand grams. The prefixmilli-,likewise, may be added tometreto indicatedivisionby one thousand; one millimetre is equal to one thousandth of a metre.
Decimal multiplicative prefixes have been a feature of all forms of themetric system,with six of these dating back to the system's introduction in the 1790s. Metric prefixes have also been used with some non-metric units. TheSI prefixesare metric prefixes that were standardised for use in theInternational System of Units(SI) by theInternational Bureau of Weights and Measures(BIPM) in resolutions dating from 1960 to 2022.[1][2]Since 2009, they have formed part of theISO/IEC 80000standard. They are also used in theUnified Code for Units of Measure(UCUM).
List of SI prefixes
editThe BIPM specifies twenty-fourprefixes for the International System of Units (SI).
| Prefix | Base 10 | Decimal | Adoption [nb 1] | |
|---|---|---|---|---|
| Name | Symbol | |||
| quetta | Q | 1030 | 1000000000000000000000000000000 | 2022[3] |
| ronna | R | 1027 | 1000000000000000000000000000 | |
| yotta | Y | 1024 | 1000000000000000000000000 | 1991 |
| zetta | Z | 1021 | 1000000000000000000000 | |
| exa | E | 1018 | 1000000000000000000 | 1975[4] |
| peta | P | 1015 | 1000000000000000 | |
| tera | T | 1012 | 1000000000000 | 1960 |
| giga | G | 109 | 1000000000 | |
| mega | M | 106 | 1000000 | 1873 |
| kilo | k | 103 | 1000 | 1795 |
| hecto | h | 102 | 100 | |
| deca | da | 101 | 10 | |
| — | — | 100 | 1 | — |
| deci | d | 10−1 | 0.1 | 1795 |
| centi | c | 10−2 | 0.01 | |
| milli | m | 10−3 | 0.001 | |
| micro | μ | 10−6 | 0.000001 | 1873 |
| nano | n | 10−9 | 0.000000001 | 1960 |
| pico | p | 10−12 | 0.000000000001 | |
| femto | f | 10−15 | 0.000000000000001 | 1964 |
| atto | a | 10−18 | 0.000000000000000001 | |
| zepto | z | 10−21 | 0.000000000000000000001 | 1991 |
| yocto | y | 10−24 | 0.000000000000000000000001 | |
| ronto | r | 10−27 | 0.000000000000000000000000001 | 2022[3] |
| quecto | q | 10−30 | 0.000000000000000000000000000001 | |
| ||||
The first uses of prefixes in SI date back to the definition of kilogram after the French Revolution at the end of the 18th century. Several more prefixes came into use, and were recognised by the 1947IUPAC14th International Conference of Chemistry[5]before being officially adopted for the first time in 1960.[6]
The most recent prefixes adopted wereronna-,quetta-,ronto-,andquecto-in 2022, after a proposal from British metrologist Richard J. C. Brown. The large prefixesronna-andquetta-were adopted in anticipation of needs for use in data science, and because unofficial prefixes that did not meet SI requirements were already circulating. The small prefixes were also added, even without such a driver, in order to maintain symmetry.[7]
The prefixes fromtera-toquetta-are based on the Ancient Greek or Ancient Latin numbers from 4 to 10, referring to the 4th through 10th powers of 103.The initial letterhhas been removed from some of these stems and the initial lettersz,y,r,andqhave been added, ascending in reverse Alpha betical order, to avoid confusion with other metric prefixes.
Rules
edit- The symbols for the units of measure are combined with the symbols for each prefix name. The SI symbols for kilometre, kilogram, and kilowatt, for instance, are km, kg, and kW, respectively. (The symbol for kilo- is k.) Except for the early prefixes ofkilo-,hecto-,anddeca-,the symbols for the prefixes for multiples are uppercase letters, and those for the prefixes for submultiples are lowercase letters.[8]
- All of the metric prefix symbols are made from upper- and lower-caseLatin lettersexcept for the symbol formicro,which is uniquely a Greek letterμ.[a]
- The prefix symbols are always prepended to the symbol for the unit without any intervening space or punctuation.[9]This distinguishes a prefixed unit symbol from the product of unit symbols, for which a space or mid-height dot as separator is required. So, for instance, while 'ms' means millisecond, 'm s' or 'm·s' means metre-second.
- Prefixes corresponding to an integer power of one thousand are generally preferred; the prefixes corresponding to tens (deci-, deca-) and hundreds (centi-, hecto-) are less common and are disfavoured in certain fields. Hence, 100 m is preferred over 1 hm (hectometre) or 10 dam (decametres). The prefixesdeci-andcenti-,and less frequentlyhecto-anddeca-,are generally used for informal purposes; the centimetre (cm) is especially common. Some modern building codes require that the millimetre be used in preference to the centimetre, because "use of centimetres leads to extensive usage of decimal points and confusion".[10]These prefixes are also commonly used to create metric units corresponding to older conventional units, for examplehectaresandhectopascals.
- Prefixes may not be used in combination on a single symbol. This includes the case of the base unit kilogram, which already contains a prefix. For example, milligram (mg) is used instead of microkilogram (μkg).
- During mathematical operations, prefixes are treated as multiplicative factors. For example, 5 km is treated as 5000 m, which allows all quantities based on the same unit to befactored togethereven if they have different prefixes.
- A prefix symbol attached to a unit symbol is included when the unit is raised to a power. For example, 1 km2denotes 1 km × 1 km = 106m2,not 103m2.
Usage
editExamples
edit- The mass of anelectronis about 1 rg (rontogram).[7][b]
- The mass of 1 litre ofwateris about 1 kg (kilogram).[12]
- The mass of theEarthis about 6 Rg (ronnagrams).[7]
- The mass ofJupiteris about 2 Qg (quettagrams).[7]
Examples of powers of units with metric prefixes
edit- 1 km2means onesquare kilometre,or theareaof asquareof1000 mby1000 m.In other words, an area of1000000square metresand not1000square metres.
- 2 Mm3means two cubicmegametres,or thevolumeof twocubesof1000000mby1000000mby1000000m,i.e.2×1018m3,and not2000000cubic metres(2×106m3).
Examples with prefixes and powers
edit- 5 mV×5 mA=5×10−3V×5×10−3A=25×10−6V⋅A=25 μW.
- 5.00 mV+10 μV=5.00 mV+0.01 mV=5.01 mV.
- 5 cm=5×10−2m=5 × 0.01 m= 0.05 m.
- 9 km2=9 × (103m)2=9 × (103)2× m2=9×106m2=9 ×1000000m2=9000000m2.
- 3 MW =3×106W= 3 ×1000000W=3000000W.
Micro symbol
editWhenmegaandmicrowere adopted in 1873, there were then three prefixes starting with "m", so it was necessary to use some other symbol besides upper and lowercase 'm'. Eventually the Greek letter "μ" was adopted.
However, with the lack of a "μ" key on most typewriters, as well as computer keyboards, various other abbreviations remained common, including "mc", "mic", and "u".
From about 1960 onwards, "u" prevailed in type-written documents.[c]BecauseASCII,EBCDIC,and other common encodings lacked code-points for "μ",this tradition remained even as computers replaced typewriters.
WhenISO 8859-1was created, it included the "μ"symbol formicroat codepoint0xB5;later, the whole of ISO 8859-1 was incorporated into the initial version ofUnicode.Many fonts that support both characters render them identical, but because the micro sign and the Greek lower-case letter have different applications (normally, a Greek letter would be used with other Greek letters, but the micro sign is never used like that), some fonts render them differently, e.g.Linux LibertineandSegoe UI.[citation needed]
Keyboard entry
editMost English-language keyboards do not have a "μ"key, so it is necessary to use a key-code; this varies depending on the operating system, physical keyboard layout, and user's language.
- For all keyboard layouts
-
- OnMicrosoft Windowssystems,
- arbitrary Unicode codepoints can be entered in decimal with:Altsustained,0181,and releasingAlt.A leading "0" is required
(this registers as the corresponding Unicode hexadecimal code-point, 0xB5 = 181.), or - arbitrary Unicode codepoints can be entered in hexadecimal as:Alt++b5
(up to 5 hexadecimal characters, not counting the leading '+', upper or lower case), or - in the tradition of MS-DOS,IBM code page 437one can also enter old code-points in decimal:Alt+230
(the leading zero must be omitted);
- arbitrary Unicode codepoints can be entered in decimal with:Altsustained,0181,and releasingAlt.A leading "0" is required
- OnLinuxsystems,
- under X11, when aCompose keyhas been enabled:Composemu
- under X11, withibusversion 1.5.19 (or higher) active, and a non-composing input method selected: The default keybinding for starting codepoint input isCtrl+⇧ Shift+u.The key sequenceCtrl+⇧ Shift+ub5spacethen produces U+00B5, the micro sign.
- on the VGA console's virtual terminals like tty1: arbitrary Unicode codepoints can be entered in decimal as:Altsustained,181,and releasingAlt.A leading "0" is not required.
- OnMicrosoft Windowssystems,
- For QWERTY keyboard layouts
Typesetting in Latex
editTheLaTeXtypesetting system features anSIunitxpackage in which the units of measurement are spelled out, for example,
\qty{3}{\tera\hertz}formats as "3 THz".[13]
Application to units of measurement
editThe use of prefixes can be traced back to the introduction of the metric system in the 1790s, long before the 1960 introduction of the SI.[citation needed]The prefixes, including those introduced after 1960, are used with any metric unit, whether officially included in the SI or not (e.g., millidyne and milligauss). Metric prefixes may also be used with some non-metric units, but not, for example, with the non-SI units of time.[14]
Metric units
editMass
editThe unitskilogram,gram,milligram,microgram, and smaller are commonly used for measurement ofmass.However, megagram, gigagram, and larger are rarely used;tonnes(and kilotonnes, megatonnes, etc.) orscientific notationare used instead. The megagram does not share the risk of confusion that the tonne has with other units with the name "ton".
The kilogram is the only coherent unit of theInternational System of Unitsthat includes a metric prefix.[15]: 144
Volume
editThelitre(equal to a cubic decimetre), millilitre (equal to a cubic centimetre), microlitre, and smaller are common. In Europe, the centilitre is often used for liquids, and the decilitre is used less frequently. Bulk agricultural products, such as grain, beer and wine, often use the hectolitre (100 litres).[citation needed]
Larger volumes are usually denoted in kilolitres, megalitres or gigalitres, or else in cubic metres (1 cubic metre = 1 kilolitre) or cubic kilometres (1 cubic kilometre = 1 teralitre). For scientific purposes, the cubic metre is usually used.[citation needed]
Length
editThe kilometre, metre, centimetre, millimetre, and smaller units are common. The decimetre is rarely used. The micrometre is often referred to by the older non-SI namemicron,which is officially deprecated. In some fields, such aschemistry,theångström(0.1 nm) has been used commonly instead of the nanometre. Thefemtometre,used mainly in particle physics, is sometimes called afermi.For large scales, megametre, gigametre, and larger are rarely used. Instead, ad hoc non-metric units are used, such as thesolar radius,astronomical units,light years,andparsecs;the astronomical unit is mentioned in the SI standards as an accepted non-SI unit.[citation needed]
Time
editPrefixes for the SI standard unitsecondare most commonly encountered for quantities less than one second. For larger quantities, the system ofminutes(60 seconds),hours(60 minutes) anddays(24 hours) isaccepted for use with the SIand more commonly used. When speaking of spans of time, the length of the day is usually standardised to86400seconds so as not to create issues with the irregularleap second.[citation needed]
Larger multiples of the second such as kiloseconds and megaseconds are occasionally encountered in scientific contexts, but are seldom used in common parlance. For long-scale scientific work, particularly inastronomy,theJulian yearorannum(a) is a standardised variant of theyear,equal to exactly31557600seconds (365+ 1 /4days). The unit is so named because it was the average length of a year in theJulian calendar.Long time periods are then expressed by using metric prefixes with the annum, such as megaannum (Ma) orgigaannum(Ga).[citation needed]
Angle
editThe SI unit of angle is theradian,butdegrees,as well asarc-minutes and arc-seconds,see some scientific use.[citation needed]
Temperature
editCommon practice does not typically use the flexibility allowed by official policy in the case of the degree Celsius (°C). NIST states:[16]"Prefix symbols may be used with the unit symbol °C and prefix names may be used with the unit namedegree Celsius.For example, 12 m°C (12 millidegrees Celsius) is acceptable. "In practice, it is more common for prefixes to be used with thekelvinwhen it is desirable to denote extremely large or small absolute temperatures or temperature differences. Thus, temperatures of star interiors may be given with the unit of MK (megakelvin), and molecular cooling may be given with the unit mK (millikelvin).[citation needed]
Energy
editIn use thejouleand kilojoule are common, with larger multiples seen in limited contexts. In addition, thekilowatt-hour,a composite unit formed from thekilowattand hour, is often used for electrical energy; other multiples can be formed by modifying the prefix of watt (e.g. terawatt-hour).[citation needed]
There exist a number of definitions for the non-SI unit, thecalorie.There are gram calories and kilogram calories. One kilogram calorie, which equals one thousand gram calories, often appears capitalised and without a prefix (i.e.Cal) when referring to "dietary calories"in food.[17]It is common to apply metric prefixes to the gram calorie, but not to the kilogram calorie: thus, 1 kcal = 1000 cal = 1 Cal.
Non-metric units
editMetric prefixes are widely used outside the metric SI system. Common examples include themegabyteand thedecibel.Metric prefixes rarely appear withimperialorUSunits except in some special cases (e.g., microinch, kilofoot,kilopound). They are also used with other specialised units used in particular fields (e.g.,megaelectronvolt,gigaparsec,millibarn,kilodalton). In astronomy, geology, and palaeontology, theyear,with symbol 'a' (from the Latinannus), is commonly used with metric prefixes:ka,Ma, and Ga.[18]
Official policies about the use of SI prefixes with non-SI units vary slightly between theInternational Bureau of Weights and Measures(BIPM) and the AmericanNational Institute of Standards and Technology(NIST). For instance, the NIST advises that "to avoid confusion, prefix symbols (and prefix names) are not used with the time-related unit symbols (names) min (minute), h (hour), d (day); nor with the angle-related symbols (names) ° (degree), ′ (minute), and ″ (second)",[16]whereas the BIPM adds information about the use of prefixes with the symbolasfor arcsecond when they state: "However astronomers use milliarcsecond, which they denote mas, and microarcsecond, μas, which they use as units for measuring very small angles."[19]
Non-standard prefixes
edit
Obsolete metric prefixes
editSome of the prefixes formerly used in the metric system have fallen into disuse and were not adopted into the SI.[20][21][22]The decimal prefix for ten thousand,myria-(sometimes speltmyrio-), and the earlybinary prefixes[broken anchor]double-(2×) anddemi-(1/2×) were parts of the original metric system adopted by France in 1795,[23][d] but were not retained when the SI prefixes were internationally adopted by the 11thCGPM conferencein 1960.
Other metric prefixes used historically includehebdo-(107) andmicri-(10−14).
Double prefixes
editDouble prefixes have been used in the past, such asmicromillimetresormillimicrons(nownanometres),micromicrofarads(μμF; nowpicofarads,pF),kil Omega tonnes(nowgigatonnes),hectokilometres(now 100kilometres) and the derived adjectivehectokilometric(typically used for qualifying the fuel consumption measures).[24]These are not compatible with the SI.
Other obsolete double prefixes included "decimilli-" (10−4), which was contracted to "dimi-"[25]and standardised in France up to 1961.
There are no more letters of the Latin Alpha bet available for new prefixes (all the unused letters are already used for units). As such, Richard J.C. Brown (who proposed the prefixes adopted for 10±27and 10±30) has proposed a reintroduction of compound prefixes (e.g.kiloquetta-for 1033) if a driver for prefixes at such scales ever materialises, with a restriction that the last prefix must always bequetta-orquecto-.This usage has not been approved by the BIPM.[26][27]
Similar symbols and abbreviations
editIn written English, the symbolKis often used informally to indicate a multiple of thousand in many contexts. For example, one may talk of a40K salary(40000), or call theYear 2000 problemtheY2K problem.In these cases, an uppercase K is often used with an implied unit (although it could then be confused with the symbol for the kelvin temperature unit if the context is unclear). This informal postfix is read or spoken as "thousand", "grand", or just "k".
The financial and general news media mostly use m or M, b or B, and t or T as abbreviations for million, billion (109) and trillion (1012), respectively, for large quantities, typically currency[28]and population.[29]
Themedicalandautomotivefields in the United States use the abbreviationsccorccmfor cubic centimetres. Onecubic centimetreis equal to onemillilitre.
For nearly a century, engineers used the abbreviationMCMto designate a "thousandcircular mils"in specifying the cross-sectional area of largeelectrical cables.Since the mid-1990s,kcmilhas been adopted as the official designation of a thousand circular mils, but the designationMCMstill remains in wide use. A similar system is used in natural gas sales in the United States:m(orM) for thousands andmm(orMM) for millions ofBritish thermal unitsortherms,and in the oil industry,[30]whereMMbblis the symbol for "millions of barrels". This usage of the capital letterMfor "thousand" is fromRoman numerals,in whichMmeans 1000.[31]
See also
edit- Binary prefix– Symbol placed before units of digital information to indicate multiplication by a power of two
- CJK Compatibility– Unicode block (U+3300-33FF) containing various characters composed into ideographic squares, and embedding Japanese Katakana words, or digits and ideographs for dates, or symbols with Latin letters for measurement units
- E1 series (preferred numbers)– Series of preferred values for passive electrical components
- Engineering notation– A version of scientific notation in which the exponent of ten reflects powers of a thousand
- Indian numbering system– Indian methods of naming large numbers
- International vocabulary of metrology– Committee under the chairmanship of the director of the BIPM
- ISO/IEC 80000– Published standard series about physical quantities and units of measurement
- Numeral prefix– Prefix derived from numerals or other numbers
- Order of magnitude– Scale of numbers with a fixed ratio
- Orders of magnitude (data)– Computer data measurements and scales
- RKM code– Notation to specify resistor and capacitor values
- Unified Code for Units of Measure– System of codes for unambiguously representing measurement units
Footnotes
edit- ^ForASCIIcompatibility in general text usage,μis frequently substituted with the Latin letteru.
- ^me=9.1093837139(28)×10−31kg[11].Converting to grams gives9.1093837015×10−28g.Rounding to the nearest power of ten gives1×10−27g,or 1 rg.
- ^ Sometimes the symbol 'u' is marked by adding a downstroke using a pen or pencil, or a slash '/u'.
- ^ "Art. 8. Dans les poids et mesures de capacité, chacune des mesures décimales de ces deux genres aura son double et sa moitié, afin de donner à la vente des divers objets toute la commodité que l'on peut désirer. Il y aura donc le double-litre et le demi-litre, le double-hectogramme et le demi-hectogramme, et ainsi des autres.
References
edit- ^"SI prefixes".Bipm.org.Bureau International des Poids et Mesures. Archived fromthe originalon 2014-09-12.Retrieved2023-06-13.
- ^"Resolutions of the General Conference on Weights and Measures (27th meeting)"(PDF)(in French and English). Bureau International des Poids et Mesures. 2022-11-18.Archivedfrom the original on 2023-06-13.Retrieved2024-05-18.
- ^ab"On the extension of the range of SI prefixes".2022-11-18.Retrieved2023-02-05.
- ^"Metric (SI) Prefixes".NIST.
- ^Comptes rendus de la Quatorzième Conférence(in French). London:IUPAC.1947-07-24.
- ^"Resolution 12 of the 11th meeting of the CGPM".Bipm.org.Bureau International des Poids et Mesures. 1960. Archived fromthe originalon 2013-02-13.Retrieved2023-09-12.
- ^abcdSample, Ian (2022-11-18),"Earth weighs in at six ronnagrams as new prefixes picked for big and small",The Guardian,retrieved2022-12-14
- ^"Metric Prefixes and SI Units".learn.sparkfun.tutorials.Retrieved2020-01-26.
- ^"SI Unit rules and style conventions checklist".nist.gov.NIST.September 2004 [February 1998].
- ^Metric Design Guide(PDF)(Report). Public Buildings Service. U.S.General Services Administration.September 1995. PBS-PQ260. Archived fromthe original(PDF)on 2011-12-15.Retrieved2018-04-21– via National Institute of Building Sciences.
- ^"2022 CODATA Value: electron mass".The NIST Reference on Constants, Units, and Uncertainty.NIST.May 2024.Retrieved2024-05-18.
- ^"Kilogram | mass, weight, SI unit | Britannica".2024-03-15.
- ^Kottwitz, Stefan (2015-10-28),LaTeX Cookbook,Packt Publishing Ltd, pp. 158–9,ISBN978-1-78439-630-5
- ^The International System of Units(PDF)(9th ed.), International Bureau of Weights and Measures, Dec 2022, p. 145,ISBN978-92-822-2272-0
- ^The International System of Units(PDF)(9th ed.), International Bureau of Weights and Measures, Dec 2022,ISBN978-92-822-2272-0
- ^abThompson, Ambler; Taylor, Barry N. (March 2008).Special Publication 811(Report) (2008 ed.).National Institute of Standards and Technology.Retrieved2018-06-21– via nist.gov.
- ^Conn, Carole; Kravitz, Len."Remarkable Calorie".University of New Mexico.Retrieved2017-05-22.
- ^Gargaud, Muriel; Amils, Ricardo; Cleaves, Henderson James (26 May 2011). "Ga".Encyclopedia of Astrobiology.Springer Science & Business Media. p. 621.ISBN978-3-642-11271-3.
- ^The International System of Units (SI)(Report). SI Brochure. International Bureau of Weights and Measures.Retrieved2017-03-05.
- ^"H.R. 596, An Act to authorize the use of the metric system of weights and measures".29th Congress of the United States, Session 1. 1866-05-13. Archived fromthe originalon 2015-07-05.
- ^Brewster, David (1830).The Edinburgh Encyclopædia.Vol. 12. Edinburgh, UK: William Blackwood, John Waugh, John Murray, Baldwin & Cradock, J.M. Richardson. p. 494.Retrieved2015-10-09.
- ^Brewster, David (1832).The Edinburgh Encyclopaedia.Vol. 12 (1st American ed.). Joseph and Edward Parker.Retrieved2015-10-09.
- ^"La loi du 18 Germinal an 3".L'histoire du mètre[The History of the Metre] (in French).Archivedfrom the original on 2022-11-26.Retrieved2015-10-12– via histoire.du.metre.free.fr.
Décision de tracer le mètre, unité fondamentale, sur une règle de platine. Nomenclature des « mesures républicaines ». Reprise de la triangulation
[The Law of 18 Germinal [month], Year 3: Decision to draw the fundamental unit metre on a platinum ruler. Nomenclature of "republican measures". Resumption of the triangulation] - ^Rowlett, Russ (2008) [2000]."millimicro-".How Many? A dictionary of units of measurement.University of North Carolina at Chapel Hill.Archivedfrom the original on 2016-08-29.Retrieved2016-08-29.
- ^Danloux-Dumesnils, Maurice (1969).The Metric System: A critical study of its principles and practice.The Athlone Press. p. 34.ISBN9780485120134.Retrieved2015-10-09.(a translation of the French originalEsprit et bon usage du système métrique,1965 )
- ^Brown, Richard J.C. (2022-04-27). "Reply to" Facing a shortage of the Latin letters for the prospective new SI symbols: Alternative proposal for the new SI prefixes "".Accreditation and Quality Assurance.27(3): 143–144.doi:10.1007/s00769-022-01499-7.S2CID248397680.
- ^Brown, Richard J.C. (2019). "Considerations on compound SI prefixes".Measurement.140:237–239.Bibcode:2019Meas..140..237B.doi:10.1016/j.measurement.2019.04.024.S2CID146092009.
- ^"Obama unveils $3.8T budget proposal".Canadian Broadcasting Corporation. Associated Press. 2012-02-13.Retrieved2012-03-01.
- ^"More than 65M Flock to Discovery's Planet Earth".Multichannel.Retrieved2012-03-01.
- ^"Purcell, P (2007).Disambiguating M.PESA News 88 ".Pesa.au. Archived fromthe originalon 2012-03-25.Retrieved2012-03-01.
- ^"What is the difference between MCM and kcmil?".Reference. 2015-08-04.Retrieved2016-09-05.
