SI prefix

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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.

Contents 1 Overview 2 Pronunciation 3 Use outside SI 3.1 Non-SI units 3.2 Computing 4 Proposed changes 4.1 Extension 4.2 Harmonization 5 Popular culture 6 See also 7 References 8 External links

Overview

SI defines a number of SI prefixes to be used with the 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 above 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.

Template:SI prefixes

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

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".

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 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 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 reason various fields have develop their own non-SI scales is because of the problems posed by calculating very large or very small numbers on a computer accurately and efficiently. 1 angstrom is a lot easier for a computer to use in calculations than 1 × 10^-10 as truncation errors and rounding errors can occur losing accuracy in the calculation.

^† 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.

Pronunciation

The accepted English pronunciation of the initial G of giga was once soft, Template:IPA (like giant), but now the hard pronunciation, Template:IPA (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.

Since 'kilometre' is a combined word, it should logically be pronounced with a stress on the first syllables of the composite words (kIlomEtre), as in the other units, such as 'kilogram', but it is not uncommon in the English language to put the stress on the 'o' (kilOmetre).

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

Template:Main

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 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 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’, 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 nove. This does not have the convenience of backward alphabetic order.

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 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 giga-watt was one such example, 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 the fact that Americans seem to prefer the hard G.

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 Moore's Law 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

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 unitsbr:Rakgerioù ar SI

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