Si prefix



This article needs additional citations for verification. Please help improve this article by adding reliable references. Unsourced material may be challenged and removed. (January 2008)

An SI prefix (also known as a metric prefix) is a name or associated symbol that precedes a basic unit of measure (or its symbol) to form a decimal multiple or submultiple. The abbreviation SI is from the French language name Système International d’Unités (also known as International System of Units). SI prefixes are used to reduce the number of zeros shown in numerical quantities. For example, one-billionth of an ampere (a small electrical current) can be written as 0.000 000 001 ampere. In symbol form, this is written as 0.000 000 001 A. Using an SI prefix, this is equivalent to 1 nanoampere or 1 nA. The SI prefixes are governed by the Bureau International des Poids et Mesures (BIPM, also known as the International Bureau of Weights and Measures) and are the product of four resolutions dating from 1960 to 1991.

List of SI prefixes

The twenty SI prefixes are shown in the chart below.

Usage

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.

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)." ¹ 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." ²

SI prefixes with °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.

Details

See also: Non-SI unit prefixes

Examples:

• 5 cm = 5 × 10⁻² m = 5 × 0.01 m = 0.05 m
• 3 MW = 3 × 10⁶ W = 3 × 1 000 000 W = 3 000 000 W

The prefix always takes precedence over any exponentiation; thus "km²" means square kilometre and not kilo–square metre. For example, 3 km² is equal to 3 000 000 m² and not to 3,000 m² (nor to 9 000 000 m²). Thus the SI prefixes provide steps of a factor one million instead of one thousand in the case of an exponent 2, of a thousand million in the case of an exponent 3, etc. As a result quite large or small numbers may be needed, even if full advantage is taken of the prefixes, unless intermediate units (like the litre) are introduced.

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.

The 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, no one-letter symbol was available (M, m, and µ already being used; the two-letter symbols mo and ma were used instead) and were rarely used anyway.

The prefix kilo derives from the Greek word χίλια (khilia or chilia) = thousand.

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 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.

^† 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.

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).^{3 4}

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 /kɨˈlɒmɨtɚ/, with reduced vowels on both syllables of metre.

Use outside SI

The symbol "K" is often used informally to mean a multiple of (a) thousand, so one may talk of "a 40K salary" (40 000), or the Y2K problem. In these cases an uppercase K is often used, although using an uppercase K is never correct when writing under the rules of the SI. Also, it is often used as a prefix to designate the binary prefix kilo = 2¹⁰ = 1024, although this is now non-standard.

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.

Computing

Main article: Binary prefix

The prefixes k and greater are common in computing, where they are applied to information and storage units like the bit and the byte. Since 2¹⁰ = 1024, and 10³ = 1000, this led to the SI prefix letters being used to denote "binary" powers. Although these are incorrect usages according to the SI standards it seems common to apply base 10 prefixes, when relating to computer memory, as follows:

kilo (k) 

≈ kibi = Ki = 2¹⁰ = 1024¹ = 1 024;

mega (M) 

≈ mebi = Mi = 2²⁰ = 1024² = 1 048 576;

giga (G) 

≈ gibi = Gi = 2³⁰ = 1024³ = 1 073 741 824;

tera (T) 

≈ tebi = Ti = 2⁴⁰ = 1024⁴ = 1 099 511 627 776 (= 1 024 Gi);

peta (P) 

≈ pebi = Pi = 2⁵⁰ = 1024⁵ = 1 125 899 906 842 624 (= 1 048 576 Gi);

exa (E) 

≈ exbi = Ei = 2⁶⁰ = 1024⁶ = 1 152 921 504 606 846 976 (= 1 073 741 824 Gi).

These prefixes, however, usually retain their powers-of-1000 meanings when used to describe either disk storage or rates of data transmission (bit rates): 10 Mbit/s Ethernet runs at 10,000,000 bit/s, not 10,485,760 bit/s. This creates confusion when the two usages in memory or filesystems and in transmission or disk storage are colliding, notably for monitoring file transmission rates.

The confusion is compounded by the fact that the units of information (the bit and the byte) are not part of SI, where the bit, byte, octet, baud or symbol rate would rather be given in hertz. Although some use "bit" for the bit and "b" for the byte, "b" is often used for bit and "B" for byte instead. The baud symbol is normally "Bd" but it is often confused with bits per second and abbreviated with just its initial, in either letter case, even though it does not directly measure the effective binary data rate but the way this data is encoded and modulated over a transmission link.

It is recommended by several standards bodies to not abbreviate bit and to use B for byte, in order to keep the units very distinct, as in kbit or MiB.⁵ French-speakers often use "o" for "octet", today a near synonym for the byte.

Consequently, 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), formed from the first syllable of the decimal prefix plus 'bi' (pronounced 'bee'). The symbol is the decimal symbol (converted to capital for the first prefix) plus 'i'.

• So now, one kilobyte (1 kB) equals 1000 bytes, whereas one kibibyte (1 KiB) equals 2¹⁰ = 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 practical use of these binary prefixes is growing slowly and is largely limited to expert literature. Their use in marketing literature is rare.

Proposed changes

There are proposals for further harmonisation of the capitalisation. Therefore the symbols for kilo, hecto, and deka 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, deka, 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 ubiquitous in common use: 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).

See also

References

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

External links

Standards organisations

• The International Bureau of Weights and Measures (BIPM): SI prefixes
• 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"

Other proposals

• 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 organisation).