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.

Not all such prefixes are exclusive to SI. Many SI prefixes, and the very idea of using prefixes for this purpose, predate the introduction of the SI in 1960, so they are also quite properly used with many non-SI units.

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

Table of contents

1 Overview 2 Pronunciation 3 Use outside SI 3.1 Non-SI units 3.2 Computing 4 Proposed extensions 5 See also 6 References 7 External links

Overview

As an 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 (1000 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.

SI prefixes

10n	Prefix	Symbol	Short scale	Long scale Name	Decimal Equivalent
1024	yotta	Y	Septillion	Quadrillion	1 000 000 000 000 000 000 000 000
1021	zetta	Z	Sextillion	Trilliard (thousand trillion)	1 000 000 000 000 000 000 000
1018	exa	E	Quintillion	Trillion	1 000 000 000 000 000 000
1015	peta	P	Quadrillion	Billiard (thousand billion)	1 000 000 000 000 000
1012	tera	T	Trillion	Billion	1 000 000 000 000
109	giga	G	Billion	Milliard (thousand million)	1 000 000 000
106	mega	M	Million		1 000 000
103	kilo	k	Thousand		1 000
102	hecto	h	Hundred		100
101	deca, deka	da	Ten		10
10−1	deci	d	Tenth		0.1
10−2	centi	c	Hundredth		0.01
10−3	milli	m	Thousandth		0.001
10−6	micro	µ	Millionth		0.000 001
10−9	nano	n	Billionth	Milliardth	0.000 000 001
10−12	pico	p	Trillionth	Billionth	0.000 000 000 001
10−15	femto	f	Quadrillionth	Billiardth	0.000 000 000 000 001
10−18	atto	a	Quintillionth	Trillionth	0.000 000 000 000 000 001
10−21	zepto	z	Sextillionth	Trilliardth	0.000 000 000 000 000 000 001
10−24	yocto	y	Septillionth	Quadrillionth	0.000 000 000 000 000 000 000 001
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See also: Obsolete metric 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

Prefixes cannot be combined: for example 10⁻⁹ metre must be written as 1 nm, not as 1 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 3000 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 m" rather than "1 hm". Notable exceptions include centimetre, hectare (hecto-are), centilitre, cubic decimetre (equivalent to one litre), hectopascal, and decibel (one-tenth of a bel). 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.

Double prefixes such as micromicrofarads (picofarads), hectokilometres (100 kilometres), and millimicrons or micromillimetres (both nanometres) were also dropped with the introduction of the SI.

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 1/1000 of this object's mass.

Though in principle legal, most combinations of prefixes with quantities are very rarely used, even in a scientific or engineering context:

• Mass: hectogram, gram, milligram, microgram, and smaller are common. However, megagram or larger are rarely used; tonnes or scientific notation are used instead. Megagram is sometimes 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.
• Length: kilometre, metre, decimetre, centimetre, millimetre, and smaller are common. 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.

^† Britain, 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. 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.

Pronunciation

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

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

• 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 except in some specialised cases (e.g. microinches, kilofeet).
• 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 (ab-)used 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, where the bit, byte, octet, baud or symbol rate would rather be given in hertz. 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", nowadays 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.

Proposed extensions

Continuing backwards in the alphabet, after zetta and yotta, proposals for the next large number include xenta and xona (among others), the latter as an alteration of the Latin-derived numerical prefix , and the next small number would also start with an x.

Preserving the rule on abbreviating the prefixes (a Latin capital for the large number and a lower-case letter for the small number), even without consensus on the full name the following prefix symbols could be used without ambiguity: X, W, V, x, w, v. The logically next small prefix symbol, "u", is the accepted substitution for "µ" (ISO 2955), the symbol for "micro".

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 . This does not have the convenience of backward alphabetic order.

There are also proposals for further harmonization of the capitalisation. Therefore the symbols for deka, hecto and kilo would be changed from "da", "h" and "k" to "D" or "Da", "H" and "K" respectively. Likewise some lobby for the removal of prefixes that don't fit the 10^±3·n 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 currently. In volume measuring, for example, this inconvenience has lead to the continued use of the litre, which is one thousandth cubic metre (0.001 m³) or one cubic decimetre (1 dm³), where it could be handy to call it "one milli-cubic metre" ("1 m(m³)")—one cubic millimetre (mm³) is one billionth of a cubic metre.

See also

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

References

External links

• The International Bureau of Weights and Measures (BIPM): SI prefixes
• Proposal for an extension of the SI-prefix sytem to even larger and smaller units

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