Metric prefix

Metric prefixes in everyday use
Text	Symbol	Factor	Power
exa	E	1000000000000000000	1018
peta	P	1000000000000000	1015
tera	T	1000000000000	1012
giga	G	1000000000	109
mega	M	1000000	106
kilo	k	1000	103
hecto	h	100	102
deca	da	10	101
(none)	(none)	1	100
deci	d	0.1	10−1
centi	c	0.01	10−2
milli	m	0.001	10−3
micro	μ	0.000001	10−6
nano	n	0.000000001	10−9
pico	p	0.000000000001	10−12
femto	f	0.000000000000001	10−15
atto	a	0.000000000000000001	10−18

A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or fraction of the unit. While all metric prefixes in common use today are decadic, historically there have been a number of binary metric prefixes as well. 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 milli-, likewise, may be added to metre to indicate division by one thousand; one millimetre is equal to one thousandth of a metre.

Decimal multiplicative prefixes have been a feature of all forms of the metric system with six dating back to the system's introduction in the 1790s. Metric prefixes have even been pre-pended to non-metric units. The SI 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 have formed part of the International System of Quantities.

List of SI prefixes

The BIPM specifies twenty prefixes for the International System of Units (SI).

SI prefixes

Prefix 1000m 10n Decimal English word Adoption Name Symbol Short scale Long scale yotta Y  10008  1024 1000000000000000000000000  septillion  quadrillion 1991 zetta Z  10007  1021 1000000000000000000000  sextillion  thousand trillion or trilliard 1991 exa E  10006  1018 1000000000000000000  quintillion  trillion 1975 peta P  10005  1015 1000000000000000  quadrillion  thousand billion or billiard 1975 tera T  10004  1012 1000000000000  trillion  billion 1960 giga G  10003  109 1000000000  billion  thousand million or milliard 1960 mega M  10002  106 1000000             million 1960 (1873) kilo k  10001  103 1000             thousand 1960 (1795) hecto h  10002/3  102 100             hundred 1960 (1795) deca da  10001/3  101 10             ten 1960 (1795)  10000  100 1             one – deci d  1000−1/3  10−1 0.1             tenth 1960 (1795) centi c  1000−2/3   10−2 0.01             hundredth 1960 (1795) milli m  1000−1  10−3 0.001             thousandth 1960 (1795) micro μ  1000−2  10−6 0.000001             millionth 1960 (1873) 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 a symbol which is used in combination with the symbols for units of measure. For example, the symbol for kilo- is k, and is used to produce km, kg, and kW, which are kilometre, kilogram, and kilowatt, respectively.

Prefixes may not be used in combination. This also applies to mass, for which the SI base unit (kilogram) already contains a prefix. For example, milligram (mg) is used instead of microkilogram (µkg).

In arithmetic of measurements having prefixed units, the prefixes must be expanded to their numeric multiplier, except when adding or subtracting values with identical units. Hence, 5 mV × 5 mA = 5×10⁻³ V × 5×10⁻³ A = 25×10⁻⁶ W = 25 µW.

Prefixes corresponding to an integer power of one thousand are generally preferred. Hence 100 m is preferred over 1 hm (hectometre) or 10 dam (decametres). The prefixes hecto, deca, deci, and centi were commonly used for everyday purposes, especially the centimetre (cm) is common. However, 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".

When units occur in exponentiation, for example, in square and cubic forms, the multiplication prefix must be considered part of the unit, and thus included in the exponentiation.

• 1 km² means one square kilometre, or the area of a square of 1000 m by 1000 m and not 1000 square metres.
• 2 Mm³ means two cubic megametres, or the volume of two cubes of 1000000 m by 1000000 m by 1000000 m or 2×10¹⁸ m³, and not 2000000 cubic metres (2×10⁶ m³).

Examples

• 5 cm = 5×10⁻² m = 5 × 0.01 m = 0.05 m
• 9 km² = 9 × (10³ m)² = 9 × (10³)² × m² = 9×10⁶ m² = 9 × 1000000 m² = 9000000 m²
• 3 MW = 3×10⁶ W = 3 × 1000000 W = 3000000 W

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.

Metric units

Mass

In use, the kilogram, gram, milligram, microgram, and smaller are fairly 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.

Uniquely among SI units, the base unit of mass, the kilogram, already includes a prefix. The prefixes do not, therefore, indicate corresponding multiples of the base unit in the case of mass; for example, a megagram is 1×10³ kg, whereas mega- indicates a multiple of 10⁶.

Volume

The litre (equal to a cubic decimetre), millilitre (equal to a cubic centimetre), microlitre, and smaller are common. In Europe, the centilitre is often used for packaged products (such as wine) and the decilitre less frequently. (The latter two items include prefixes corresponding to an exponent that is not divisible by three.)

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.

Length

The kilometre, metre, centimetre, millimetre, and smaller are common. (However, the decimetre is rarely used.) 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. Instead, non-metric units are used, such as 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." The SI unit of angle is the radian, but, as mentioned above, degrees, minutes and seconds see some scientific use.

Temperature

Official policy also varies from common practice for the degree Celsius (°C). NIST states:[2] "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 are widely used outside the system of metric units. Common examples include the megabyte and the decibel. 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). 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. In English speaking countries kilometre is often 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".

Non-standard 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.

Obsolete metric prefixes

Some of the prefixes formerly used in the metric system have fallen into disuse and were not adopted into the SI. The decimal prefix myria- (sometimes also written as myrio-) (ten thousand) as well as the binary prefixes double- and demi-, denoting a factor of 2 and ​¹⁄₂ (one half), 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.

Double prefixes

Double prefixes have been used in the past, such as micromillimetres or "millimicrons" (now nanometres), micromicrofarads (now picofarads), kilomegatons (now gigatons), 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.

Other obsolete double prefixes included "decimilli-" (10⁻⁴), which was contracted to "dimi-" and standardized in France up to 1961.

"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.

X, W and V

Brian C. Lacki follows Z and Y with the adopted prefixes X, W and V to mean 10²⁷, 10³⁰ and 10³³ respectively, thus continuing the inverse alphabetical order.

Similar symbols and 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'.

Binary prefixes

In some fields of information technology it has been common to designate non-decimal multiples based on powers of 1024, rather than 1000, for some SI prefixes (kilo, mega, giga), contrary to the definitions in the International System of Units (SI). This practice has been sanctioned by some industry associations, including JEDEC. The International Electrotechnical Commission (IEC) standardized the system of binary prefixes (kibi, mebi, gibi, etc.) for this purpose.

See also

• Engineering notation
• Indian Numbering System
• International vocabulary of metrology
• ISO/IEC 80000
• 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