SI prefix

An SI prefix is a prefix which can be applied to any unit of the International System of Units (SI) to give subdivisions and multiples of that unit.

As part of the SI system they are officially determined by the Bureau International des Poids et Mesures.

Overview

For example, the prefix "kilo" multiplies by one thousand, so a kilometre is 1,000 metres, and a kilowatt is 1,000 watts. The prefix "milli" subdivides by a thousand, so a millimetre is one thousandth of a metre (1,000 millimetres in a metre), and a millilitre is one thousandth of a litre. The ability to apply the same prefixes to any SI unit is one of the key strengths of the SI, since it considerably simplifies the system's learning and use.

The most commonly used prefixes include:

giga = 10⁹, (Short scale) billion, (Long scale) milliard, a thousand million

mega = million

kilo = thousand

centi = one hundredth

milli = one thousandth

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

Prefixes cannot be combined: for example 10^-9 metre should be written as nm, not as mμm.

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 billion in the case of an exponent 3, etc. As a result large numbers may be needed, even if the prefixes are fully used.

Prefixes where the exponent is divisible by three are recommended. Hence '100 metres' rather than 'one hectometre'. Notable exceptions include centimetre, hectare (hecto-are), centilitre, 1 dm³ (equivalent to one litre), and decibel (one-tenth of a bel, a measure of sound loudness). The obsolete prefixes myria- and myrio- were dropped before SI was adopted in 1960, probably because they do not fit this pattern, no symbol was available (M, m and μ already being used), and were rarely used anyway.

The kilogram stands out among all SI base units as the only one that has a prefix. It is derived from the mass of an actual object. The gram is defined as 1/1000th of this object's mass.

Though in principle legal, quantities that are commonly used in everyday life are not combined with all possible prefixes, even when used in a scientific or engineering context:

• Mass: hg, g, mg, μg, and smaller are common. However, Mg or larger are never used; tonnes or scientific notation are used instead.
• Volume in litres: l, dl, cl, ml, μl, and smaller are common. Larger volumes are sometimes denoted in hl; otherwise in m³ or km³.
• Length: km, m, dm, cm, mm, and smaller are common. Mm, Gm, etc. are rarely used. Often used are AU, ly, pc; the AU is mentioned in the SI standards as accepted non-SI unit
• Time: s, ms, μs, and shorter are common. For longer times, one uses either scientific notation or minutes, hours, etc.

Pronunciation

The accepted English pronunciation of the initial G of giga was once soft, /ˈdʒaɪgə/ (like gigantic), but now the hard pronunciation, /ˈgɪgə/ (like giggle), is probably more common. However, both pronunciations are likely to be understood by most English speakers.

Use outside SI

The symbol "k" is often used to mean a multiple of a thousand, so one may talk of "a 40K salary" (40,000), or the Y2K problem. Note that in these cases an upper case K is often used, although it should be noted that 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.

Non-SI units

SI prefixes rarely appear coupled with imperial units except in some specialised cases (e.g. megaton). They are often used with cgs units in situations where these are still found (e.g. millitorr). They are also used with "natural" units in some fields (e.g. megaelectron volt, gigaparsec).

Computing

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 approximately to denote "binary" prefixes as follows:

k = 2¹⁰ = 1,024

M = 2²⁰ = 1,048,576

G = 2³⁰ = 1,073,741,824

T = 2⁴⁰ = 1,099,511,627,776

P = 2⁵⁰ = 1,125,899,906,842,624.

However, these prefixes usually retain their powers-of-1000 meanings when used to describe rates of data transmission (bit rates): 10 Mbit/s Ethernet runs at 10,000,000 bit/s, not 10,485,760 bit/s. The problem is compounded by the fact that the units of information (the bit and the byte) are not part of SI. Although it is clearer symbology to use "bit" for the bit and "b" for the byte, "b" is often used for bit and "B" for byte. (In SI, B stands for the bel.) French-speaking countries often use "o" for "octet", a synonym for byte, but this is unacceptable in SI because of the risk of confusion with the zero.

Consequently, the International Electrotechnical Commission (IEC) adopted new binary prefixes in 1998, formed from the first syllable of the decimal prefix plus 'bi' (pronounced 'bee'). The symbol is the decimal symbol 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), and exbi (Ei; 2⁶⁰). Although the IEC standard does not mention them, the sequence can be readily extended to zebi (Zi; 2⁷⁰) and yobi (Yi; 2⁸⁰). The adoption of these prefixes has been very limited.

^† Britain, Ireland and Australia previously used the long scale number name conventions, but have now largely switched to the short scale usage. Note in particular that above a million and below a millionth, the same name has different values in the two naming systems, so billion and trillion (for example) become unfortunately potentially ambiguous terms internationally. Using the SI prefixes can circumvent this problem. See number names for the details.

Proposed extensions

Continuing backwards in the alphabet, after zetta and yotta, proposals for the next large number include xenta and xona, the latter as an alteration of the Latin nona, and the next small number would also start with an x.

Preserving the rule on abbreviating the prefixes (a capital for the large number and a lower-case letter for the small number), even without consensus on the full name the following prefixes could be used without ambiguity: X, W, V, U, x, w, v, u. However, even some official prefixes may not be understood by all readers, let alone extrapolations of them, so giving an explanation is advisable when using them in communication (as opposed to using them in notes for oneself).

Another proposal for xenta/xona is novetta, from the Italian nove. This does not have the convenience of backward alphabetic order.

See also

• binary prefix
• engineering notation
• number names
• orders of magnitude
• numbers in various languages (for comparison/etymology)

References

External links

• The International Bureau of Weights and Measures (BIPM): SI prefixes (http://www.bipm.fr/en/si/prefixes.html)
• Calculation: Orders of Prefixes (http://www.sengpielaudio.com/ConvPref.htm)
• Proposal for an extension of the SI-prefix sytem to even larger and smaller units (http://jimvb.home.mindspring.com/unitsystem.htm)

ca:Prefixos del SI da:SI-præfiks de:Vorsilben für Maßeinheiten es:Prefijos del SI et:Ühikute_detsimaaleesliited fr:Préfixe du système international hr:Predmeci (prefiksi) mjernih jedinica hu:SI-prefixum pl:Przedrostek_SI pt:Prefixos SI sl:Predpone SI sr:СИ префикси zh-cn:国际单位制词头 zh-tw:國際單位制詞頭