Metric prefixes in everyday use

Text

Symbol

Factor

tera

T

1000000000000

giga

G

1000000000

mega

M

1000000

kilo

k

1000

hecto

h

100

deca

da

10

(none)

(none)

1

deci

d

0.1

centi

c

0.01

milli

m

0.001

micro

μ

0.000001

nano

n

0.000000001

pico

p

0.000000000001


A metric prefix or SI prefix is a unit prefix that precedes a basic unit of measure to indicate a decadic multiple or fraction of the unit. Each prefix has a unique symbol that is prepended to the unit symbol. The prefix kilo, for example, may be added to gram to indicate multiplication by one thousand; one kilogram is equal to one thousand grams. The prefix centi, likewise, may be added to metre to indicate division by one hundred; one centimetre is equal to one hundredth of a metre.
Decimal multiplicative prefixes have been a feature of all forms of the metric system with many dating back to the system's introduction in the 1790s. Metric prefixes have even been prepended to nonmetric units. Today the prefixes are standardized for use in the International System of Units (SI) by the International Bureau of Weights and Measures (BIPM) in resolutions dating from 1960 to 1991.^{[1]} Since 2009, they form part of the International System of Quantities.
List of SI prefixes
There are twenty prefixes specified by the BIPM as part of the SI.
Metric prefixes

Prefix

1000^{m}

10^{n}

Decimal

English word

Since^{[n 1]}

name

symbol

short scale

long scale

yotta

Y

1000^{8}

10^{24}

1000000000000000000000000

septillion

quadrillion

1991

zetta

Z

1000^{7}

10^{21}

1000000000000000000000

sextillion

thousand trillion

1991

exa

E

1000^{6}

10^{18}

1000000000000000000

quintillion

trillion

1975

peta

P

1000^{5}

10^{15}

1000000000000000

quadrillion

thousand billion

1975

tera

T

1000^{4}

10^{12}

1000000000000

trillion

billion

1960

giga

G

1000^{3}

10^{9}

1000000000

billion

thousand million

1960

mega

M

1000^{2}

10^{6}

1000000

million

1960

kilo

k

1000^{1}

10^{3}

1000

thousand

1795

hecto

h

1000^{2/3}

10^{2}

100

hundred

1795

deca

da

1000^{1/3}

10^{1}

10

ten

1795


1000^{0}

10^{0}

1

one

–

deci

d

1000^{−1/3}

10^{−1}

0.1

tenth

1795

centi

c

1000^{−2/3}

10^{−2}

0.01

hundredth

1795

milli

m

1000^{−1}

10^{−3}

0.001

thousandth

1795

micro

μ

1000^{−2}

10^{−6}

0.000001

millionth

1960

nano

n

1000^{−3}

10^{−9}

0.000000001

billionth

thousand millionth

1960

pico

p

1000^{−4}

10^{−12}

0.000000000001

trillionth

billionth

1960

femto

f

1000^{−5}

10^{−15}

0.000000000000001

quadrillionth

thousand billionth

1964

atto

a

1000^{−6}

10^{−18}

0.000000000000000001

quintillionth

trillionth

1964

zepto

z

1000^{−7}

10^{−21}

0.000000000000000000001

sextillionth

thousand trillionth

1991

yocto

y

1000^{−8}

10^{−24}

0.000000000000000000000001

septillionth

quadrillionth

1991




^ The metric system was introduced in 1795 with six prefixes. The other dates relate to recognition by a resolution of the CGPM.
Each prefix name has an associated symbol which can be used in combination with the symbols for units of measure. Thus, the "kilo" symbol, k, can be used to produce km, kg, and kW, (kilometre, kilogram, and kilowatt).
Prefixes may not be used in combination. This also applies to mass, for which the SI base unit (which is the kilogram, not the gram) already contains a prefix. So milligram (mg) is used instead of microkilogram (µkg), for example.
There are multiple approaches to doing multiplication and division with prefixed values. In one, prefixed values cannot be multiplied or divided together, and they have to be converted into nonprefixed standard form for such calculations, hence 5 mV × 5 mA ≠ 25 mW. In this model, the correct calculation is: 5 mV × 5 mA = 5 × 10^{−3} V × 5 × 10^{−3} A = 25 x 10^{−6} W = 25 µW = 0.025 mW. Another approach is to treat prefixes as representative of their underlying values, and manipulate them algebraically. 5 mV × 5 mA = 25 mW is still incorrect, since one of the "m" prefixes has been erroneously dropped rather than being squared; the correct calculation is 5 mV × 5 mA = 25 m^{2}W (only one prefix is allowed, so either the numeric must be multiplied by 10^{−3} or the m^{2} converted to µ) = .025 mW or 25 µW. Algebraic prefix manipulation may introduce ambiguity if the symbols for prefixes aren't kept distinct from those for units.
Prefixes corresponding to an exponent that is divisible by three are often recommended. Hence "100 m" rather than "1 hm" (hectometre) or "10 dam" (decametres). The "nonthree" prefixes (hecto, deca, deci, and centi) are however more commonly used for everyday purposes than in science.
When units occur in exponentiation, for example, in square and cubic forms, the size prefix is considered part of the unit, and thus included in the exponentiation.

Examples

5 cm = 5×10^^{−2} m = 5×0.01m = 0.05m

9 km^{2} = 9×(km)^{2} = 9×k^{2}m^{2} = 9×(10^{3})^{2}×m^{2} = 9×10^^{6} m^{2} = 9×1000000m^{2} = 9000000m^{2}

3 MW = 3×10^^{6} W = 3×1000000W = 3000000W
Application to units of measurement
The 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. The prefixes, including those introduced after 1960, are used with any metric unit, whether officially included in the SI or not (e.g. millidynes and milligauss). Metric prefixes may also be used with nonmetric units.
The choice of prefixes with a given unit is usually dictated by convenience of use. Unit prefixes for amounts that are much larger or smaller than those actually encountered are seldom used, though they remain valid combinations. In most contexts only a few most common combinations are established as standard.

Mass
The kilogram, hectogram, gram, milligram, microgram, and smaller are common. However, megagram (and gigagram, teragram, etc.) are rarely used; tonnes (and kilotonnes, megatonnes, etc.) or scientific notation are used instead. Megagram is occasionally used to disambiguate the metric tonne from the various nonmetric tons. An exception is pollution emission rates, which are typically on the order of Tg/yr. Sometimes only one element is denoted for an emission, such as Tg C/yr or Tg N/yr, so that intercomparisons of different compounds are easier.

Volume
The litre, decilitre, centilitre, millilitre or cubic centimetre, microlitre, and smaller are common. Larger volumes are sometimes denoted in hectolitres; otherwise in cubic metres or cubic kilometres. In Australia, large quantities of water are measured in kilolitres, megalitres and gigalitres.

Length
The kilometre, metre, decimetre, centimetre, millimetre, and smaller are common. The micrometre is often referred to by the nonSI term micron. In some fields such as chemistry, the angstrom (equal to 0.1 nm) historically competed with the nanometre. The femtometre, used mainly in particle physics, is usually called a fermi. For large scales, megametre, gigametre, and larger are rarely used. Often used are astronomical units, light years, and parsecs; the astronomical unit is mentioned in the SI standards as an accepted nonSI unit.

Time and angles
The second, millisecond, microsecond, and shorter are common. The kilosecond and megasecond also have some use, though for these and longer times one usually uses either scientific notation or minutes, hours, and so on.
Official policies about the use of these prefixes vary slightly between the Bureau International des Poids et Mesures (BIPM) and the American National Institute of Standards and Technology (NIST); and some of the policies of both bodies are at variance with everyday practice. For instance, the NIST advises that "…to avoid confusion, prefix symbols (and prefixes) are not used with the timerelated unit symbols (names) min (minute), h (hour), d (day); nor with the anglerelated symbols (names) ° (degree), ′ (minute), and ″ (second)." ^{[2]}
The BIPM’s position on the use of SI prefixes with units of time larger than the second is the same as that of the NIST but their position with regard to angles differs: they state "However astronomers use milliarcsecond, which they denote mas, and microarcsecond, µas, which they use as units for measuring very small angles." ^{[3]}

Temperature
Official policy also varies from common practice for the degree Celsius (°C). NIST states; "Prefix symbols may be used with the unit symbol °C and prefixes may be used with the unit name 'degree Celsius'. For example, 12 m°C (12 millidegrees Celsius) is acceptable." In practice, it is more common for prefixes to be used with the kelvin when it is desirable to denote extremely large or small absolute temperatures or temperature differences. Thus, temperatures of star interiors may be given in units of MK (megakelvins), and molecular cooling may be described in mK (millikelvins).

Energy
There exist a number of definitions for the nonSI unit, the calorie. There are gram calories and kilogram calories. One kilogram calorie, which equals one thousand gram calories, often appears capitalized and without a prefix (i.e. 'Cal') when referring to "dietary calories" in food. It is common to apply metric prefixes to the gram calorie but not to the kilogram calorie: thus, for example, 1 kcal = 1000 cal = 1 Cal.
Nonmetric units
Metric prefixes rarely appear with imperial or US units except in some special cases (e.g., microinch, kilofoot, kilopound or 'kip'). They are also used with other specialized units used in particular fields (e.g., megaelectronvolt, gigaparsec, millibarn, decibel). They are also occasionally used with currency units (e.g., gigadollar), mainly by people who are familiar with the prefixes from scientific usage.
Presentation
Pronunciation
The prefix giga is usually pronounced but sometimes . According to the American writer /dʒ/ (soft g) pronunciation was accepted, but as of 1995 current practice had returned to /ɡ/ (hard g).^{}[4] ^{[5]}
When an SI prefix is affixed to a root word, the prefix carries the stress, while the root drops its stress but retains a full vowel in the syllable that is stressed when the root word stands alone. For example, gigabyte is , with stress on the first syllable. However, words in common use outside the scientific community may follow idiosyncratic stress rules. Kilometre is commonly pronounced /kɨˈlɒmɨtər/, with reduced vowels on both syllables of metre.
Typesetting
The LaTeX typesetting system features an SIunitx package, in which the units of measurement are spelled out, for example, \SI{3}{\tera\hertz}
formats as 3 THz.
Disallowed and obsolete prefixes
Former metric prefixes
Some of the prefixes formerly used in the metric system have fallen into disuse and were not adopted into the SI.^{[6]}^{[7]} The prefix myria (ten thousand) originated from the Greek μύριοι (mýrioi) (myriad), and the prefixes demi and double, denoting a factor of ^{1}⁄_{2} and 2, respectively,^{[8]} were parts of the original metric system adopted by France in 1795. These were not retained when the SI prefixes were internationally adopted by the 11th CGPM conference in 1960. The halving and doubling prefixes were dropped because they were neither decimal nor symmetrical. Most were rarely used, although the myriametre (10 km) is occasionally encountered in 19thcentury train tariffs, or in some classifications of wavelengths as the adjective myriametric. In Sweden and Norway, the myriametre is still common in everyday use. In these countries this unit is called mil. Of units customarily used in trade in France, the myriagramme (10 kg) was the metric replacement for an avoirdupois unit, the quartier (25 pounds). Isaac Asimov's novel Foundation and Empire mentions the myriaton.
Double prefixes
Double prefixes have been used in the past, such as micromillimetres or "millimicrons" (now nanometres), micromicrofarads (now picofarads), hectokilometres (now 100 kilometres) and the derived adjective hectokilometric (typically used for qualifying the fuel consumption measures).^{[9]} These were disallowed with the introduction of the SI.
"Hella" prefix proposal
In 2010, UC Davis student Austin Sendek started a petition to designate "hella" as the SI prefix for one octillion (10^{27}).^{[10]} The petition gathered over 60,000 supporters by circulating through Facebook and receiving a significant amount of media coverage.^{[11]} Although the Consultative Committee for Units considered the proposal, it was ultimately rejected. However, hella has been adopted by certain websites, such as Google Calculator^{[12]} and Wolfram Alpha.^{[13]}
Similar symbols in abbreviations
In written English, the symbol K is often used informally to mean a multiple of thousand in many contexts. For example, one may talk of a 40K salary (40000), or call the Year 2000 problem the Y2K problem. In these cases an uppercase K is often used. This informal postfix is read or spoken as "thousand" or "grand", or just "k", but never "kilo" (despite that being the origin of the letter).
The financial and general news media mostly use m/M, b/B and t/T as abbreviations for million, billion (10^{9}) and trillion (10^{12}) for large quantities, typically currency^{[14]} and population. ^{[15]}
The medical and automotive fields in the United States use the abbreviations "cc" or "ccm" for cubic centimetres. 1 cubic centimetre is equivalent to 1 millilitre. Most nations use millilitres in preference to cubic centimetres.
For nearly a century, the electrical construction industry used the abbreviation "MCM" to designate a "thousand circular mils" in specifying thicknesses of large electrical cables. Since the mid1990s, "kcmil" has been adopted as the "official" designation of a thousand circular mils, but the designation "MCM" still remains in wide use. A similar system is used in natural gas sales in the United States: m (or M) for thousands and mm (or MM) for millions of British thermal units or therms, and in the oil industry,^{[16]} where 'MMbbl' is the symbol for 'millions of barrels'.
The computer industry is possibly the only industry in which some SI prefixes have been given definitions inconsistent with the International System of Units (SI). JEDEC has redefined the prefixes kilo, mega and giga as powers of 1024 instead of 1000, but not tera or any larger decimal prefix. With an aim of avoiding confusion, the International Electrotechnical Commission has defined a different set of binary names and symbols for the same powerof1024 units.^{[17]}^{[Note 1]}
See also
Notes

^ The names and symbols of the binary prefixes proposed by the IEC include

kibi (Ki) = 2^{10} = 1024

mebi (Mi) = 2^{20} = 1024^{2} = 1048576

gibi (Gi) = 2^{30} = 1024^{3} = 1073741824
etc.
References
This article is based on material taken from the Free Online Dictionary of Computing prior to 1 November 2008 and incorporated under the "relicensing" terms of the GFDL, version 1.3 or later.

^ "Four Resolutions". Bipm.org. Retrieved 1 March 2012.

^ http://physics.nist.gov/Pubs/SP811/sec06.html

^ "BIPM  SI prefixes". Bipm.fr. Retrieved 1 March 2012.

^ Self, Kevin (October 1994). "Technically speaking". Spectrum (IEEE): 18.

^ Self, Kevin (April 1995). "Technically speaking". Spectrum (IEEE): 16.

^ 29th Congress of the United States, Session 1 (13 May 1866). "H.R. 596, An Act to authorize the use of the metric system of weights and measures".

^ D. Brewster (1830). The Edinburgh Encyclopaedia. p. 494.

^ "histoire.du.metre.free.fr". histoire.du.metre.free.fr. Retrieved 1 March 2012.

^ Rowlett, Russ (28 May 2010). "millimicro". How Many? A Dictionary of Units of Measurement. Retrieved 30 October 2010.

^ Steve Chawkins (6 July 2010). "Physics major has a name for a really big number". Los Angeles Times.

^ "The Official Petition to Establish "Hella" as the SI Prefix for 10^27".

^ Ryan Kim. "Google gets behind "hella" campaign". SFGate.

^ Austin Sendek. "First goes Google, now goes Wolfram Alpha".

^ The Associated Press (13 February 2012). "Obama unveils $3.8T budget proposal". Cbc.ca. Retrieved 1 March 2012.

^ "More than 65M Flock to Discovery's Planet Earth". Multichannel.com. Retrieved 1 March 2012.

^ "Purcell, P (2007). ''Disambiguating M''. PESA News 88". Pesa.com.au. Retrieved 1 March 2012.

^ International Electrotechnical Commission (January 2010). "IEC 60050  International Electrotechnical Vocabulary  Details for IEV number 1120127". Retrieved 19 June 2011.
External links

Bureau International des Poids et Mesures (BIPM)

SI prefixes at BIPM

Definitions of the SI units: The twenty SI prefixesUS NIST

Definitions of the SI units: The binary prefixesUS NIST

International Standard ISO 2955: "Information processing  Representation of SI and other units in Systems with limited Character sets"[Withdrawn]
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