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The International System of Units (SI) specifies a set of unit prefixes, known as SI prefixes, also known as metric prefixes. An SI prefix is a name that precedes a basic unit of measure to indicate a decimal multiple or fraction of the unit. Each prefix has a unique symbol that is prepended to the unit symbol. The SI prefixes are standardized by the International Bureau of Weights and Measures in resolution dating from 1960 to 1991.^[1]

SI prefixes are used to reduce the number of zeros shown in numerical quantities before or after the decimal point. For example, an electrical current of 0.000000001ampere, or one-billionth (short scale) of an ampere, is written by using the SI-prefix nano as 1 nanoampere or 1 nA.

Contents 1 List of SI prefixes 1.1 Examples 2 General use of prefix names and symbols 3 SI prefixes with symbols for time and angles 4 SI prefixes for temperature in °C 5 Exponentiation of symbols 6 Pronunciation 7 Other and obsolete prefixes 7.1 Non-SI units 7.2 Similar prefixes as abbreviations 8 Units used in computing and telecommunications 8.1 Binary prefixes 9 Proposed changes 10 See also 11 References 12 External links

[edit] List of SI prefixes

The International System of Units specifies twenty SI prefixes:

SI prefixes

1000m	10n	Prefix	Symbol	Since[1]	Short scale	Long scale	Decimal
10008	1024	yotta	Y	1991	Septillion	Quadrillion	1000000000000000000000000
10007	1021	zetta	Z	1991	Sextillion	Trilliard	1000000000000000000000
10006	1018	exa	E	1975	Quintillion	Trillion	1000000000000000000
10005	1015	peta	P	1975	Quadrillion	Billiard	1000000000000000
10004	1012	tera	T	1960	Trillion	Billion	1000000000000
10003	109	giga	G	1960	Billion	Milliard	1000000000
10002	106	mega	M	1960	Million		1 000 000
10001	103	kilo	k	1795	Thousand		1000
10002⁄3	102	hecto	h	1795	Hundred		100
10001⁄3	101	deca	da	1795	Ten		10
10000	100	(none)	(none)	NA	One		1
1000−1⁄3	10−1	deci	d	1795	Tenth		0.1
1000−2⁄3	10−2	centi	c	1795	Hundredth		0.01
1000−1	10−3	milli	m	1795	Thousandth		0.001
1000−2	10−6	micro	µ	1960[2]	Millionth		0.000001
1000−3	10−9	nano	n	1960	Billionth	Milliardth	0.000000001
1000−4	10−12	pico	p	1960	Trillionth	Billionth	0.000000000001
1000−5	10−15	femto	f	1964	Quadrillionth	Billiardth	0.000000000000001
1000−6	10−18	atto	a	1964	Quintillionth	Trillionth	0.000000000000000001
1000−7	10−21	zepto	z	1991	Sextillionth	Trilliardth	0.000000000000000000001
1000−8	10−24	yocto	y	1991	Septillionth	Quadrillionth	0.000000000000000000000001
The metric system was introduced in 1795 with six prefixes. The other dates relate to recognition by a resolution of the CGPM. The 1948 recognition of the micron by the CGPM was abrogated in 1967.

[edit] Examples

• 5 cm = 5×10^⁻² m = 5×0.01m = 0.05m
• 3 MW = 3×10^⁶ W = 3×1000000W = 3000000W

[edit] General use of prefix names and symbols

Twenty SI prefixes are available to combine with units of measure. For example, the prefix kilo- denotes a multiple of one thousand, so 1 kilometre equals 1000 metres, 1 kilogram equals 1000 grams, 1 kilowatt equals 1000 watts, and so on. Each SI 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). SI prefixes are internationally recognized and also exist outside the SI (many of them long pre-date SI, going back to the original introduction of the metric system); prefixes may also be used in combination with non-SI units; for example: milligauss (mG), kilofoot (kft) and microinch (µin).

Prefixes may not be used in combination. This even applies for 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.

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.

[edit] SI prefixes with symbols for time and angles

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)." ^[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]

[edit] SI prefixes for temperature in °C

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." However the use of prefixed forms of "°C" (such as "µ°C") has not been adopted in science and engineering; prefixed forms of the kelvin (which are precisely equivalent) are usually used instead.

[edit] Exponentiation of symbols

When units occur in exponentiation, for example, in square and cubic forms, any size prefix is considered part of the unit, and thus included in the exponentiation.

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

[edit] Pronunciation

There are two accepted pronunciations for the prefix giga-: /ˈɡɪɡə/ and /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 at what point the /dʒ/ (soft g) pronunciation became 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 pronounced /ˈɡɪɡəbaɪt/, with stress on the first syllable. However, words in common use outside the scientific community may follow idiosyncratic stress rules. For example, kilometre is commonly pronounced /kɨˈlɒmɨtər/, with reduced vowels on both syllables of metre.

[edit] Other and obsolete prefixes

Obsolete prefixes such as myrio- and myria-, denoting a factor of 10,000, were dropped before SI was adopted in 1960, probably because they did not fit this pattern. A one-letter symbol was not available, as M, m, and µ were already used, so the two-letter symbols mo and ma were, albeit rarely, used instead.

Double prefixes such as those formerly used in micromicrofarads (picofarads), hectokilometres (100 kilometres), and millimicrons or micromillimetres (both nanometres) were also dropped with the introduction of the SI.

Though in principle valid, many combinations of prefixes with quantities are rarely used (in many cases because the quantity they represent is larger or smaller than encountered in practice). In most contexts only a few, i.e. the most common, standard combination are established:

• Mass: hectogram, gram, milligram, microgram, and smaller are common. However, megagram or larger are rarely used; tonnes (and kilotonnes etc) or scientific notation are used instead. Megagram is occasionally used to disambiguate the (metric) tonne from the various (non-metric) tons.
• Volume in litres: 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: 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 ångström (equal to 0.1 nm) competes 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: 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.

^† the United Kingdom, Ireland, Australia and New Zealand previously used the long scale number name conventions, but have now at least partly switched to the short scale usage. In particular, above a million and below a millionth, the same name has different values in the two naming systems, so billion and trillion (for example) have unfortunately become potentially ambiguous terms internationally. Using the SI prefixes can circumvent this problem.

[edit] Non-SI units

• Prefixes go back to the introduction of the metric system in the 1790s, long before the SI was introduced in 1960. The prefixes (including those introduced after the introduction of SI) are used with any metric units, SI or not (e.g. millidynes).
• SI prefixes rarely appear coupled with imperial units or English units except in some specialised cases (e.g. microinches, kilofeet, kilopound or 'kip').
• They are also used with other specialized units used in particular fields (e.g. megaelectronvolts, gigaparsecs).
• They are also occasionally used with currency units (e.g., gigadollar), mainly by people who are familiar with the prefixes from scientific usage.

[edit] Similar prefixes as abbreviations

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 (40 000), or call the Year 2000 problem as Y2K problem. In these cases an uppercase K is often used, although the uppercase K is the official symbol of the kelvin.

In other financial and business contexts, the letter M is often used to denote multiplication by 1000, in recognition of the Latin term mille. In these situations one million is often written as 1 MM. Similar usage of M occurs in the term CPM (Cost per mille) used in advertising.

[edit] Units used in computing and telecommunications

The International System of Units does not define symbols for the storage size units bit and byte and this has allowed ambiguities to emerge in combination with SI prefixes. The bit is often given the symbol bit or b, while byte is usually written as byte, B, and occasionally as b. Thus, kb/s sometimes means kilobits per second, but may sometimes refer to kilobytes per second.

The National Institute of Standards and Technology in the United States has suggested the use of bit for bits and B for bytes.^[6]

In non-standard use, K is often used as a symbol prefix to the units bit and byte to designate the binary prefix kibi = 2¹⁰ = 1024.

[edit] Binary prefixes

The prefixes kilo, mega, giga and greater are often used in combination with the storage size units bit and byte.

Because 2¹⁰ = 1024 which is close to the value (1000) of the prefix kilo, a 1024-byte amount of computer memory is often referred to as a kilobyte even though this does not conform to the strict definition of kilo. Likewise 2²⁰ is 1 048 576 which is close to 1 000 000 and this has led to 1 048 576 bytes often being called a megabyte. This has led to some confusion because megabyte is also used to refer to 1 000 000 bytes, e.g., in descriptions of hard disk drive capacities and network transmission bit rates.

To eliminate this ambiguity the International Electrotechnical Commission (IEC) adopted new binary prefixes in 1998 (IEC 80000-13:2008 formerly subclauses 3.8 and 3.9 of IEC 60027-2:2005). Each binary prefix is formed from the first syllable of the decimal prefix with the similar value, and the syllable 'bi' (pronounced 'bee'). Its symbol is the decimal symbol, always capitalized, followed by the letter 'i'.

According to this standard one kilobyte (1 kB) is 1000 bytes, whereas one kibibyte (1 KiB) is 1024 bytes. Likewise mebi (Mi; 2²⁰), gibi (Gi; 2³⁰), tebi (Ti; 2⁴⁰), pebi (Pi; 2⁵⁰), exbi (Ei; 2⁶⁰), zebi (Zi; 2⁷⁰) and yobi (Yi; 2⁸⁰).

The use of these new binary prefixes is increasing^{[citation needed]} but is largely limited to technical literature and new computer software.

[edit] Proposed changes

There are proposals for further harmonisation of the capitalisation. Therefore the symbols for kilo, hecto, and deca would be changed from ‘k’ to ‘K’, from ‘h’ to ‘H’, and from ‘da’ to ‘D’. Likewise some lobby for the removal of prefixes that do not fit the 10^±3n scheme, namely hecto, deca, deci, and centi. The CGPM has postponed its decision on both matters for now.

An unsolved (and maybe unsolvable) issue is the application of prefixes to units with exponents other than ±1. The prefix is always applied before the exponent. This eventually led to the introduction of special units for area and volume without exponents in the original metric system:

• 1 are (a) = 100 m² (10 m × 10 m = 1 dam × 1 dam = 1 dam²)
  • ⇒ 1 ca = 1 m² (1 m × 1 m)
  • ⇒ 1 ha = 10 000 m² (100 m × 100 m = 1 hm × 1 hm = 1 hm²)
• 1 stere (st) = 1 m³
• 1 litre (l or L) = 1 dm³ = 1 mst = 0.001 m³

Of these the litre and the hectare are the most common. Litre designations are sometimes used to differentiate a volume of liquid (as opposed to a gas, or solid which are usually designated as cubic volumes). Hectares are widely used as a metric alternative to the acre (approximately 2.5 acres to the hectare).

[edit] See also

• Binary prefix
• Engineering notation
• Metric system
• Non-SI unit prefix
• Number names
• Numbers in various languages (for comparison/etymology)
• Orders of magnitude
• Scientific notation
• SI base unit
• SI derived unit

[edit] References

This article was originally based on material from the Free On-line Dictionary of Computing, which is licensed under the GFDL.

[edit] 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]
• ISO 1000:2004 "SI Units and recommendations for the use of their multiples and of certain other units"
• Proposal for an extension of the SI-prefix system to even larger and smaller units, by a computer scientist (not an official proposal by an organization).