SI prefix

An SI prefix (also known as a metric prefix) is a name or associated symbol that precedes a unit of measure (or its symbol) to form a decimal multiple or submultiple. The abbreviation SI is from the French language name Système International d’Unités (also known as International System of Units). SI prefixes are used to reduce the quantity of zeros in numerical equivalencies. For example, one-billionth of an ampere (a small electrical current) can be written as 0.000 000 001 ampere. In symbol form, this is written as 0.000 000 001 A. Using an SI prefix, these are equivalent to 1 nanoampere and 1 nA. The SI prefixes are governed by the Bureau International des Poids et Mesures (BIPM, also known as the International Bureau of Weights and Measures) and are the product of four resolutions dating from 1960 to 1991.

List of SI prefixes

The twenty SI prefixes are shown in the below chart.

Usage

General use of prefix names and symbols

Twenty SI prefixes are available to combine with units of measure. For example, the prefix name kilo denotes a multiple of one thousand, so 1 kilometre equals 1000 metres, 1 kilogram equals 1000 grams, 1 kilowatt equals 1000 watts, and so on. Each SI prefix name has an associated symbol which can be used in combination with the symbols for units of measure. Thus, the “kilo” symbol, k, can be used to produce km, kg, and kW, (kilometre, kilogram, and kilowatt). SI prefixes are internationally recognized and may also be used in combination with non-SI units; for example: milligauss (mG), kilofoot (kft) and microinch (µin).

Prohibition of multiple prefixes

The kilogram is the only SI unit that has an SI prefix as part of its unit name and symbol. Because multiple prefixes may not be used (such as microkilogram or µkg), the prefixes are used with the unit gram and its symbol g (e.g. milligram or mg).

SI prefixes with symbols for time and angles

Officially endorsed policies of the National Institute of Standards and Technology (NIST) and the BIPM vary slightly with respect to the use of the SI prefixes—both between their respective agencies and from real–world practice. For instance, the NIST advises that “…to avoid confusion, prefix symbols (and prefixes) are not used with the time-related unit symbols (names) min (minute), h (hour), d (day); nor with the angle-related symbols (names) ° (degree), ′ (minute), and ″ (second).” The BIPM’s position on the use of SI prefixes with units of time larger than the second mirrors that of the NIST but their position with regard to angles differs: they state “However astronomers use milliarcsecond, which they denote mas, and microarcsecond, µas, which they use as units for measuring very small angles.”

SI prefixes with °C

A similar difference between officially endorsed policy and actual practice exists with regard to the symbol for degree Celsius (°C). The NIST states “Prefix symbols may be used with the unit symbol °C and prefixes may be used with the unit name ‘degree Celsius.’ For example, 12 m°C (12 millidegrees Celsius) is acceptable.” Notwithstanding this official endorsement, the practice of using prefixed forms of “°C” (such as “µ°C”) has not been well–adopted in science and engineering; prefixed forms of the kelvin are usually used instead.

Details

See also: Non-SI unit 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

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, or intermediate units (like the litre) are introduced.

Prefixes where the exponent is divisible by three are often recommended. Hence "100 m" rather than "1 hm".

The obsolete prefix myria- (and alleged counterpart myrio-) was dropped before SI was adopted in 1960, probably because it does not fit this pattern, no symbol was available (M, m, and µ already being used), and was rarely used anyway.

The prefix kilo derives from the Greek word χίλια (khilia or chilia) = 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.

Though in principle legal, many combinations of prefixes with quantities are rarely used. In most contexts only a few, i.e. the most common, standard combination are established:

• 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. In particular, 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.

Pronunciation

There are two accepted pronunciations for the prefix giga-: [ˈgɪgə] and [ˈdʒɪgə]. The former is now more common than the latter.^[1]

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 [ˈgɪgəˌbaɪt]. 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 [kəˈlɑmətɚ].

Use outside SI

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. In these cases an uppercase K is often used, although 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, 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

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 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

= 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.

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 confusion 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-speakers 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 changes

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”.^[2][3]

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 do not fit the 10^±3n 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. 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 dam²)
  • ⇒ 1 ca = 1 m² (1 m × 1 m)
  • ⇒ 1 ha = 10,000 m² (100 m × 100 m = 1 hm × 1 hm = 1 hm²)
• 1 stere (st) = 1 m³
• 1 litre (l) = 1 dm³ = 1 mst = 0.001 m³

Of 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).

Popular culture

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. [ˈdʒɪgəˌwɑt], JIGA-wot) 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' preference for [g] instead of [dʒ] 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.

See also

• 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

References

This article was originally based on material from the Free On-line Dictionary of Computing, which is licensed under the GFDL.

1. ^ Self, Kevin (October 1994). "Technically speaking". Spectrum: 18.
2. ^ International Standard ISO 2955: "Information processing - Representation of SI and other units in Systems with limited character sets (2nd ed.) pp. 4. International Organization for Standardizaton (1983-05-15). Retrieved on 2006-07-26.
3. ^ 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).

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
• 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"

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