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SI Prefixes

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.

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, US billion or European milliard, a thousand million

mega = million

kilo = thousand

centi = one hundredth

milli = one thousandth

The full table follows below.

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).

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, /ˈdʒaɪgə/ (like "gigantic"), but now the hard pronunciation, /ˈgɪgə/, is probably more common.

Note that the formal SI metric prefix for 1000 is lower case "k".

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 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

k and greater are common in computing, where they are applied to information and storage units like the bit and the byte. Since these often naturally come in powers of two, the prefixes' meaning changes:

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 communication (bit rates): 10 Mb/s Ethernet runs at 10,000,000 b/s, not 10,485,760 b/s.

This inconsistency did not seem 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.

Accordingly, the International Electrotechnical Commission 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 (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. The adoption of these prefixes has been very limited.

^† 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) become 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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