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 by the International Bureau
of Weights and Measures 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. 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,.
Prefixes may not be used in combination. This also applies to mass, for which the SI base
unit already contains a prefix. So milligram is used instead of microkilogram, 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 = .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" or "10 dam".
The "non-three" prefixes 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. 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. 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 are rarely used; tonnes 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, 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 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 and the American National
Institute of Standards and Technology; 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 are not used with the time-related unit symbols min, h, d; nor with the angle-related
symbols °, ′, and ″." 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. 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 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, and molecular cooling may be described in mK.
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 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. They are also used with other specialized
units used in particular fields. They are also occasionally used with currency units,
mainly by people who are familiar with the prefixes from scientific usage.
Presentation Pronunciation
The prefix giga is pronounced in two acceptable ways, and . 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 edition of Galgenlieder. This suggests a hard German
g was originally intended as the pronunciation. Self was unable to ascertain when the pronunciation
was accepted, but as of 1995 current practice had returned to .
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 , 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}
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. The prefix myria-
originated from the Greek μύριοι, 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
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 was the metric replacement for an avoirdupois
unit, the quartier. 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", micromicrofarads, hectokilometres and the
derived adjective hectokilometric. 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. 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, 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".
The financial and general news media mostly use m/M, b/B and t/T as abbreviations for
million, billion and trillion for large quantities, typically currency and population.
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 for thousands and 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. 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
Notes
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
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]