SI prefix

SI prefixes in everyday use
Text Symbol Factor tera T 1000000000000 giga G 1000000000 mega M 1000000 kilo k 1000 hecto h 100 (none) (none) 1 centi c 0.01 milli m 0.001 micro μ 0.000001 nano n 0.000000001

The International System of Units (SI) specifies a set of unit prefixes known as SI prefixes or metric prefixes. An SI prefix is a name 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 SI prefixes are standardized by the International Bureau of Weights and Measures in resolutions dating from 1960 to 1991.^[1] Their usage is not limited to SI units and many of these date back to the introduction of the metric system in the 1790s.

SI prefixes are used to reduce the number of zeros shown in numerical quantities before or after a 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 1nanoampere or 1nA.

List of SI prefixes

The International System of Units specifies twenty SI prefixes:

SI prefixes

Prefix	Symbol	1000m	10n	Decimal	Short scale	Long scale	Since[n 1]
yotta	Y	10008	1024	1000000000000000000000000	Septillion	Quadrillion	1991
zetta	Z	10007	1021	1000000000000000000000	Sextillion	Trilliard	1991
exa	E	10006	1018	1000000000000000000	Quintillion	Trillion	1975
peta	P	10005	1015	1000000000000000	Quadrillion	Billiard	1975
tera	T	10004	1012	1000000000000	Trillion	Billion	1960
giga	G	10003	109	1000000000	Billion	Milliard	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	Milliardth	1960
pico	p	1000−4	10−12	0.000000000001	Trillionth	Billionth	1960
femto	f	1000−5	10−15	0.000000000000001	Quadrillionth	Billiardth	1964
atto	a	1000−6	10−18	0.000000000000000001	Quintillionth	Trillionth	1964
zepto	z	1000−7	10−21	0.000000000000000000001	Sextillionth	Trilliardth	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.

Examples

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

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.

Prefixed values cannot be multiplied or divided together, and they have to be converted into non-prefixed standard form for such calculations. For example, 5 mV × 5 mA ≠ 25 mW. 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.

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.

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]

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."

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).

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 /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.

Disallowed and obsolete prefixes

See also: Non-SI unit prefixes

The prefix myria- 'ten thousand' ^[6][7] denoting a factor of 10000, originated from the Greek μύριοι (mýrioi) for ten thousand, and the prefixes demi and double, denoting a factors 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 binary prefixes were dropped because they were neither decimal nor symmetrical.

Double prefixes such as those formerly used in micromicrofarads (picofarads), hectokilometres (100 kilometres), and millimicrons or micromillimetres (both nanometres) were disallowed with the introduction of the SI. The choice of commonly used prefixes with a given unit is usually dictated by convenience of use, unit prefixes that are much larger or smaller than encountered in practice, are seldom used, albeit valid combinations. In most contexts only a few, the most common, standard combination are established:

• Mass: kilogram, 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. An exception is 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 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 angstrom (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.

Non-SI units

The use of prefixes can be traced 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 the SI, are used with any metric units, whether officially included in the SI or not (e.g., millidynes).

SI prefixes rarely appear with imperial units or English units except in some special 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.

Similar symbols in 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 (meaning one thousand), also used in roman numerals. In these situations one million is often written as 1 MM. In other financial situations, one M can mean million, such as £2M or £2m which is equal to £2 000 000. Similar usage of M occurs in the term CPM (Cost per mille) used in advertising.

For nearly a century, the electrical construction industry used the acronym "MCM" to designate a "thousand circular mils" in specifying thicknesses of large electrical cables. Since the mid-1990s, the term "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 Btus or Therms.

Units used in computing and telecommunications

The International System of Units does not define units of information, such as the storage size units bit and byte. This has allowed ambiguities to emerge with respect to the symbols in use, as well as their usage and meaning in combination with the 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 often 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.^[9] The use of 'b' for 'bytes' is ambiguous and should be strongly discouraged.

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.

Binary prefixes

Main article: Binary prefix

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

The binary multiple 2¹⁰ = 1024 is close to the value 1000 of the prefix kilo, therefore computer professionals have historically used the unit kilobyte to refer to 1024 bytes of computer memory, in non-conformance with the SI definition of the prefix kilo. Likewise, 2²⁰ = 1048576, which is close to 1000000 has been expressed with the mega prefix. This has led to some confusion, because megabyte is commonly used to refer to 1000000bytes in the specifications of hard disk drive capacities and network transmission bit rates. Although it is common to size disk drives in MB or GB(10⁶ or 10⁹) and refer to capacity as "megabytes" or "gigabytes", this has led to a number of lawsuits from purchasers who were expecting 2²⁰ or 2³⁰ and considered themselves shortchanged by the seller. To protect themselves, some sellers actually write out the full term as "1,000,000" or "1,000,000,000".

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'). The symbols are the decimal symbol, always capitalized, followed by the letter 'i'.

According to this standard one kilobyte (1 kB) is 10³ or 1000 bytes, whereas one kibibyte (1 KiB) is 2¹⁰ or 1024 bytes. Likewise mebi (Mi; 2²⁰ or 1048576), gibi (Gi; 2³⁰ or 1073741824), 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,^[10] but is largely limited to technical literature and new computer software.^{[citation needed]}

Related proposals

In 2010, an online petition sought to establish hella as the SI prefix for 10²⁷.^[11] The prefix, which has since appeared in the San Francisco Chronicle, Daily Telegraph, Wired and some other scientific magazines, was recognized by Google in May 2010.^[12][13][14] Ian Mills, president of the Consultative Committee on Units, considers the chances of official adoption to be remote.^[15]

See also

• International vocabulary of metrology
• ISO/IEC 80000
• International System of Units
• SI base unit
• SI derived unit
• Binary prefix
• Engineering notation
• Metric system
• Non-SI unit prefixes
• Number names
• Names of large numbers
• Names of small numbers
• List of numbers in various languages (for comparison/etymology)
• Order of magnitude
• Scientific notation
• Number prefix

References

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

1. ^ Four Resolutions
2. ^ http://physics.nist.gov/Pubs/SP811/sec06.html
3. ^ http://www.bipm.fr/en/si/si_brochure/chapter3/prefixes.html
4. ^ Self, Kevin (October 1994). "Technically speaking". Spectrum (IEEE): 18. 
5. ^ Self, Kevin (April 1995). "Technically speaking". Spectrum (IEEE): 16. 
6. ^ 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". http://lamar.colostate.edu/~hillger/laws/metric-act-bill.html. 
7. ^ D. Brewster (1830). The Edinburgh Encyclopaedia. p. 494. http://books.google.com/books?id=h6miHpDMjXEC&pg=PA494. 
8. ^ histoire.du.metre.free.fr
9. ^ Ambler Thompson, Barry N. Taylor. (2008). Guide for the Use of the International System of Units (SI). Gaithersburg, MD: National Institute of Standards and Technology p. 74. This source recommends B as a symbol for byte, but is silent concerning bits.
10. ^ Sadat Karim, neowin.net (27 March 2010). "Ubuntu implements units policy, will switch to base-10 units in future release". http://www.neowin.net/news/ubuntu-implements-units-policy-will-switch-to-base-10-units-in-future-release. 
11. ^ Moore, Matthew (2 March 2010). "Hella number: scientists call for new word for 1,000,000,000,000,000,000,000,000,000". The Telegraph. http://www.telegraph.co.uk/science/science-news/7352204/Hella-number-scientists-call-for-new-word-for-1000000000000000000000000000.html. Retrieved 4 June 2010. "More than 20,000 scientists, students and members of the public have signed an online petition backing the new quantity, which would be used for figures with 27 zeros after the first digit." 
12. ^ "Jargon Watch". Wired 18 (6). June 2010. "...a proposed metric prefix...useful for describing mega-measurements like Earth's mass (6 Hellagrams). A Facebook petition garnered 30,000 signatures" 
13. ^ "The Official Petition to Establish "Hella-" as the SI Prefix for 10^27". Facebook. http://www.facebook.com/pages/The-Official-Petition-to-Establish-Hella-as-the-SI-Prefix-for-1027/277479937276?v=info. Retrieved 4 June 2010. 
14. ^ Kim, Ryan (24 May 2010). "Google gets behind 'hella' campaign". The San Francisco Chronicle. http://www.sfgate.com/cgi-bin/blogs/techchron/detail?&entry_id=64240. Retrieved 4 June 2010. 
15. ^ Chawkins, Steve (6 June 2010). "Physics major has a name for a really big number". Los Angeles Times. p. 2. http://articles.latimes.com/2010/jul/06/local/la-me-hella-20100706/2. 

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).