Metric prefix

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 pre-pended to non-metric 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. 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 1000m 10n Decimal English word Since name symbol short scale long scale yotta Y  10008  1024 1000000000000000000000000  septillion  quadrillion 1991 zetta Z  10007  1021 1000000000000000000000  sextillion  thousand trillion 1991 exa E  10006  1018 1000000000000000000  quintillion  trillion 1975 peta P  10005  1015 1000000000000000  quadrillion  thousand billion 1975 tera T  10004  1012 1000000000000  trillion  billion 1960 giga G  10003  109 1000000000  billion  thousand million 1960 mega M  10002  106 1000000             million 1960 kilo k  10001  103 1000             thousand 1795 hecto h  10002/3  102 100             hundred 1795 deca da  10001/3  101 10             ten 1795  10000  100 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

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 non-prefixed 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 m²W (only one prefix is allowed, so either the numeric must be multiplied by 10⁻³ or the m² 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 "non-three" 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.

• 1km² means one square kilometre, or the area of a square of 1000 m by 1000 m and not 1000 square metres.
• 2Mm³ means two cubic megametres, or the volume of two cubes of 1000000m by 1000000m by 1000000m or 2×10^¹⁸ m³, and not 2000000cubic metres (2×10^⁶ m³).

Examples

• 5 cm = 5×10^⁻² m = 5×0.01m = 0.05m
• 9 km² = 9×(km)² = 9×k²m² = 9×(10³)²×m² = 9×10^⁶ m² = 9×1000000m² = 9000000m²
• 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 non-metric 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 non-metric 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 inter-comparisons 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 non-SI 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 non-SI 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 time-related unit symbols (names) min (minute), h (hour), d (day); nor with the angle-related symbols (names) ° (degree), ′ (minute), and ″ (second)."

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."

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 non-SI 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.

Non-metric 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 /ˈɡɪɡə/ but sometimes /ˈdʒɪɡə/. According to the American writer Kevin Self, in the 1920s a German committee member of the International Electrotechnical Commission proposed giga as a prefix for 10⁹, drawing on a verse by the humorous poet Christian Morgenstern that appeared in the third (1908) edition of Galgenlieder (Gallows Songs). This suggests a hard German g was originally intended as the pronunciation. Self was unable to ascertain when the /dʒ/ (soft g) pronunciation was accepted, but as of 1995 current practice had returned to /ɡ/ (hard g).

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 /ˈɡɪɡəbaɪt/, 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

Distance marker on the Rhine: 36 (XXXVI) myriametres from Basel. Note that the stated distance is 360 km; comma is the decimal mark in Germany.

Former metric prefixes

Some of the prefixes formerly used in the metric system have fallen into disuse and were not adopted into the SI. 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, 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 19th-century 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). 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 (10²⁷). The petition gathered over 60,000 supporters by circulating through Facebook and receiving a significant amount of media coverage. 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 and Wolfram Alpha.

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 (10⁹) and trillion (10¹²) for large quantities, typically currency and population.

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 mid-1990s, "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, 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 power-of-1024 units.

See also

• Crore (10,000,000)
• Engineering notation
• Indian Numbering System
• International vocabulary of metrology
• ISO/IEC 80000
• Lakh (100,000)
• List of numbers in various languages (for comparison/etymology)
• Names of large numbers
• Names of small numbers
• Number names
• Numeral prefix
• Order of magnitude

References

This article is based on material taken from the Free On-line Dictionary of Computing prior to 1 November 2008 and incorporated under the "relicensing" terms of the GFDL, version 1.3 or later.

External links

• Bureau International des Poids et Mesures (BIPM)
• SI prefixes at BIPM
• US NIST Definitions of the SI units: The twenty SI prefixes
• US NIST Definitions of the SI units: The binary prefixes
• International Standard ISO 2955: "Information processing - Representation of SI and other units in Systems with limited Character sets"[Withdrawn]