SI prefix
An
SI prefix is a prefix that can be applied to an
SI unit to form a decimal multiple or submultiple.
Many SI prefixes predate the introduction of the SI in 1960. They can be applied correctly to many non-SI units.
As part of the SI system they are officially determined by the
Bureau International des Poids et Mesures.
SI defines a number of SI prefixes to be used with the
SI units: these combine with any unit name to give subdivisions and multiples. As an example, the prefix
kilo denotes a multiple of a thousand, so the
kilometre is 1000
metres, the
kilogram is 1000
grams, a
kilowatt is 1000
watts, and so on. 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 prefixes are never combined; a millionth of a kilogram is a
milligram, and not a 'microkilogram'. 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 following SI prefixes can be used to prefix any of the
SI units to produce a multiple or submultiple of the original unit. This includes the degree Celsius (e.g., "1.2 m°C"); however, to avoid confusion, prefixes are
not used with the time-related unit symbols min (minute), h (hour), d (day). They are not recommended for use with the angle-related symbols ° (degree), ′ (minute of arc), and ″ (second of arc)[
1], but for astronomical usage, they are sometimes used with seconds of arc.
Examples:
* 5 cm = 5 × 10
âˆ'2 m = 5 × 0.01 m = 0.05 m
* 3 MW = 3 × 10
6 W = 3 × 1 000 000 W = 3 000 000 W
Prefixes cannot be combined: for example 10
âˆ'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
kiloâ€"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".
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 prefix
kilo derives from the
Greek words
χίλια (
khilia) = thousand.
Double prefixes such as those formerly used in
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. In Australia, large quantities of water are measured in kilolitres and megalitres.
* Length: kilometre, metre, decimetre, centimetre, millimetre, and smaller are common. The micrometre is still often incorrectly referred to as a
micron. In some fields such as
chemistry, the
angstrom (equal to 0.1 nm) competes with the nanometre. The femtometre, used mainly in particle physics, is usually called a
fermi. At large scales, 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.
†the United Kingdom, 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) have unfortunately become potentially ambiguous terms internationally. Using the SI prefixes can circumvent this problem.
There are two accepted pronunciations for the prefix
giga-: and . The former is more common than the latter.
When any SI prefix is affixed to a root word, the prefix carries the primary
stress, and the root word carries a secondary stress on the same syllable that is stressed when the root word stands alone. For example, the pronunciation and stress of
gigabyte is . However, when a word with an SI prefix is also commonly used outside the scientific community, it may adopt other pronunciations that do not follow this rule. For example,
kilometer may also be pronounced .
The symbol "K" is often used informally 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 = 2
10 = 1024, although this is now non-standard.
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
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 2
10 = 1024, and 10
3 = 1000, this led to the SI prefix letters being used to denote "binary" powers. Although these are incorrect usages according to the SI standards it seems common to apply base 10 prefixes, when relating to computers, as follows:
; K:= 2
10 = 1 024
M:= 220 = 1 048 576; G:= 2
30 = 1 073 741 824
T:= 240 = 1 099 511 627 776; P:= 2
50 = 1 125 899 906 842 624.
These prefixes, however, 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 some use "bit" for the
bit and "b" for the
byte, "b" is often used for bit and "B" for byte instead. (In SI, B stands for the
bel, although its sub-unit, the decibel ("dB"), is almost universally used instead, preventing confusion between the symbols.) It is recommended by several standards bodies to use
bit and
B to keep the units very distinct, as in
kbit or
MiB. 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 2
10 = 1024 bytes. Likewise
mebi (Mi; 2
20),
gibi (Gi; 2
30),
tebi (Ti; 2
40),
pebi (Pi; 2
50), and
exbi (Ei; 2
60). Although the IEC standard does not mention them, the sequence can be readily extended to
zebi (Zi; 2
70) and
yobi (Yi; 2
80). The adoption of these prefixes has been very limited.
Extension
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 nona-, 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', was formerly the accepted substitution for ‘µ' (now withdrawn), the symbol for "micro".
[A search at http://www.iso.org/iso/en/CatalogueListPage.CatalogueList?scopelist=CATALOGUE for standard number 2955 shows this standard is withdrawn (accessed 2006-07-26).]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. Also, the symbol 'n' is already in use for "nano".
Harmonization
There are also proposals for further harmonization of the capitalisation. Therefore the symbols for deka, hecto and kilo would be changed from ‘k' to ‘K', from ‘h' to ‘H', and from ‘da' to ‘D'. Likewise some lobby for the removal of prefixes that don't fit the 10
±3n scheme, namely hecto, deka, deci and centi. The
CGPM has tabled 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. This eventually lead to the introduction of special units for area and volume without exponents in the original
metric system:
* 1
are (a) = 100 m² (10 m × 10 m = 1 dam × 1 dam)
** ⇒ 1 ca = 1 m² (1 m × 1 m)
** ⇒ 1 ha = 10,000 m² (100 m × 100 m = 1 hm × 1 hm)
* 1
stere (st) = 1 m³
* 1
litre (l) = 1 dm³ = 1 mst = 0.001 m³Of these the litre and the hectare are the most ubiquitous in common use: Litre designations are sometimes used to differentiate a volume of fluid (as opposed to a gas, or solid which are usually designated as cubic volumes). Hectares are widely used as a metric alternative to the acre (approximately 2.5 acres to the hectare).
Several prefixes have made appearances in popular culture, specifically in America, in one fashion or another which caused them to stand out.
The original pronunciation of gigawatt (i.e. ) was used in the
Back to the Future movies. This usage predated the common occurrence of gigabytes and
gigahertz in common American usage, but does not seem to have affected much Americans' prefrence for instead of in the pronunciation of the prefix
giga-.
Additionally, an American tape backup hardware company has been named
Exabyte since well before it became possible that anyone would ever need to back up that much data; how the march of progress might affect their corporate name is unknown, but see
20th Century Fox.
*
binary prefix*
engineering notation*
number names*
orders of magnitude*
numbers in various languages (for comparison/etymology)
*
non-SI unit prefix*
SI base unit*
SI derived unit*
metric system*
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*
US NIST "Definitions of the SI units: The twenty SI prefixes"*
US NIST "Definitions of the SI units: The binary prefixes" *
International Standard ISO 2955: "Information processing - Representation of SI and other units in Systems with limited Character sets"
