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SI prefix

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

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 way that the same prefixes can be applied to any SI unit is one of the strengths of SI, since it considerable simplifies the learning and use of it.

The most commonly used are:

Giga = 10⁹, US billion or European milliard, a thousand million

Mega = million

kilo = thousand

centi = one hundredth

milli = one thousandth

The full table follows below.

(Sub)multiple Prefix Symbol Name (Americas) Name (European)

10²⁴[?] yotta Y Septillion Quadrillion

10²¹[?] zetta Z Sextillion Thousand trillion (Trilliard)

10¹⁸[?] exa E Quintillion Trillion

10¹⁵[?] peta P Quadrillion Thousand billion (Billiard[?])

10¹²[?] tera T Trillion Billion

10⁹[?] giga G Billion Thousand million (Milliard)

10⁶[?] mega M Million

10³[?] kilo k Thousand

10²[?] hecto h Hundred

10¹[?] deca or deka da Ten

10^-1[?] deci d Tenth

10^-2[?] centi c Hundredth

10^-3[?] milli m Thousandth

10^-6[?] micro μ Millionth

10^-9[?] nano n Billionth Milliardth

10^-12[?] pico p Trillionth Billionth

10^-15[?] femto f Quadrillionth Billiardth

10^-18[?] atto a Quintillionth Trillionth

10^-21[?] zepto z Sextillionth Trilliardth

10^-24[?] yocto y Septillionth Quadrillionth

Examples:

5 cm = 5 × 10^-2m = 5 × 0.01 m = 0.05 m
3 MW = 3 × 10⁶W = 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).

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, and 1 dm³ (equivalent to one litre).

The accepted pronunciation of the initial G of "giga-" was once soft, /jī'gə/ (like "gigantic"), but now the hard pronunciation, /gig'ə/, is probably more common. [Is this true of Commonwealth countries?]

Note that the formal SI metric prefix for 1000 is lower case "k"; some use this strictly, reserving "K" for multiplication by 1024 (KB is thus "kilobytes").

Use outside SI

The abbreviation "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.

Non-SI units

SI prefixes are rarely used 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

k, M and G are common in computing, where they are applied to information and storage units like the bit and the byte. Since these come in powers of two, the prefixes tend to be used differently:

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 retain their powers-of-1000 meanings when used to describe rates of data communication: 10-Mbps Ethernet runs at 10,000,000 bits per second, not 10,485,760 bits per second.

This inconsistency was not relevant when computers had little storage and communication links were relatively slow, but the increasing capacity of computing systems and speed of network links began making this inconsistency a more serious problem.

Thus, new binary prefixes have recently been adopted by the International Electrotechnical Commission, 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) is 1000 bytes, whereas one kibibyte (1 KiB) is 2¹⁰ = 1024 bytes. Likewise mebi (2²⁰), gibi (2³⁰), tebi (2⁴⁰), pebi (2⁵⁰), and exbi (2⁶⁰). For example, at 1 MB/s = 10⁶ bytes per second, it would take slightly longer than one second to transfer an object 1 MiB = 2²⁰ bytes in size.

For more information on these power-of-two prefixes, see Binary prefixes.

See also Orders of magnitude.

^† Britain, Ireland and Australia previously used the European number name conventions, but have now largely switched to US 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) are unfortunately potentially ambiguous terms internationally. Using the SI prefixes can circumvent this problem. See number names for the details.

This article (or an earlier version of it) contains material from FOLDOC, used with permission.

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