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:\n: giga = 10⁹, (Americas, UK, Ireland, Australia) billion or (Continental European) milliard, a thousand million\n: mega = million\n: kilo = thousand\n: centi = one hundredth\n: milli = one thousandth The full table follows below. \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

(Sub)multiple	Prefix	Symbol	Name (Americas, UK, Ireland, Australia)	Name (Continental 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	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:\n* 5 cm = 5 × 10^-2 m = 5 × 0.01 m = 0.05 m\n* 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, 1 dm³ (equivalent to one litre), and decibel (one-tenth of a bel, a measure of sound loudness). 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.

Table of contents

1 Use outside SI 1.1 Non-SI units 1.2 Computing 2 See also 3 External links

Use outside SI

\nThe 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, since the K stands for the Kelvin. Also, it is often used as a prefix to designate the binary prefix kilo = 2¹⁰ = 1024.

Non-SI units

\nSI 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

\nk 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\n: M = 2²⁰ = 1,048,576\n: G = 2³⁰ = 1,073,741,824\n: T = 2⁴⁰ = 1,099,511,627,776\n: 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.

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\n^† 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.

See also

\n* Binary prefixes\n* Orders of magnitude

External links

\n* The International Bureau of Weights and Measures (BIPM): SI prefixes\n* Binary prefixes \n\n\n\n\n\n\n\nzh-cn:国际单位制词头\nzh-tw:國際單位制詞頭 \nCategory:SI prefixes