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Unit prefix

## Summary

A unit prefix is a specifier or mnemonic that is prepended to units of measurement to indicate multiples or fractions of the units. Units of various sizes are commonly formed by the use of such prefixes. The prefixes of the metric system, such as kilo and milli, represent multiplication by powers of ten. In information technology it is common to use binary prefixes, which are based on powers of two. Historically, many prefixes have been used or proposed by various sources, but only a narrow set has been recognised by standards organisations.

## Metric prefixes

Prefix Symbol Factor Power
tera T 1000000000000 1012
giga G 1000000000 109
mega M 1000000 106
kilo k 1000 103
hecto h 100 102
deca da 10 101
(none) (none) 1 100
deci d 0.1 10−1
centi c 0.01 10−2
milli m 0.001 10−3
micro μ 0.000001 10−6
nano n 0.000000001 10−9
pico p 0.000000000001 10−12

The prefixes of the metric system precede a basic unit of measure to indicate a decadic multiple and fraction of a unit. Each prefix has a unique symbol that is prepended to the unit symbol. Some of the prefixes date back to the introduction of the metric system in the 1790s, but new prefixes have been added, and some have been revised. The International Bureau of Weights and Measures has standardised twenty metric prefixes in resolutions dating from 1960 to 1991 for use with the International System of Units (SI).[1] In addition to those listed in the "everyday use" table, the SI includes standardised prefixes for 1015 (peta), 1018 (exa), 1021 (zetta) and 1024 (yotta), and for 10−15 (femto), 10−18 (atto), 10−21 (zepto), and 10−24 (yocto).

Distance marker on the Rhine: 36 (XXXVI) myriametres from Basel

Although formerly in use, the SI disallows combining prefixes; the *microkilogram or *centimillimetre, for example, are not permitted. Prefixes corresponding to powers of one thousand are usually preferred, however, units such as the hectopascal, hectare, decibel, centimetre, and centilitre, are commonly used. The unit prefixes are always considered to be part of the unit, so that, e.g., in exponentiation, 1 km2 means one square kilometre, not one thousand square metres, and 1 cm3 means one cubic centimetre, not one hundredth of a cubic metre.

In general, prefixes are used with any metric unit, but may also be used with non-metric units. Some combinations, however, are more common than others. The choice of prefixes for a given unit has often arisen by convenience of use and historical developments. Unit prefixes that are much larger or smaller than encountered in practice are seldom used, albeit valid combinations. In most contexts only a few, the most common, combinations are established. For example, prefixes for multiples greater than one thousand are rarely applied to the gram or metre.

Some prefixes used in older versions of the metric system are no longer used. The prefixes myria-,[2][3][4] (from the Greek μύριοι, mýrioi), double- and demi-, denoting factors of 10000, 2 and 12 respectively,[5] were parts of the original metric system adopted in France in 1795, but they were not retained when the SI prefixes were agreed internationally by the 11th CGPM conference in 1960. The prefix "myrio-" was an alternative spelling variant for "myria-", as proposed by Thomas Young. [3][4][6][7]

## Binary prefixes

Prefixes for multiples of bits (bit) or bytes (B)
Decimal
Value SI
1000 k kilo
10002 M mega
10003 G giga
10004 T tera
10005 P peta
10006 E exa
10007 Z zetta
10008 Y yotta
Binary
Value IEC Legacy
1024 Ki kibi K kilo
10242 Mi mebi M mega
10243 Gi gibi G giga
10244 Ti tebi T tera
10245 Pi pebi
10246 Ei exbi
10247 Zi zebi
10248 Yi yobi

A binary prefix indicates multiplication by a power of two. The tenth power of 2 (210) has the value 1024, which is close to 1000. This has prompted the use of the metric prefixes kilo, mega, and giga to also denote the powers of 1024 which is common in information technology with the unit of digital information, the byte.

Units of information are not covered in the International System of Units. Computer professionals have historically used the same spelling, pronunciation and symbols for the binary series in the description of computer memory, although the symbol for kilo is often capitalised. For example, in citations of main memory or RAM capacity, kilobyte, megabyte and gigabyte customarily mean 1024 (210), 1048576 (220) and 1073741824 (230) bytes respectively.

In the specifications of hard disk drive capacities and network transmission bit rates, on the other hand, decimal prefixes, consistent with the metric system, are used. For example, a 500-gigabyte hard drive holds 500 billion bytes, and a 100-megabit-per-second Ethernet connection transfers data at 100 million bits per second. The ambiguity has led to some confusion and even of lawsuits from purchasers who were expecting 220 or 230 and considered themselves shortchanged by the seller. (see Orin Safier v. Western Digital Corporation and Cho v. Seagate Technology (US) Holdings, Inc.).[8][9] To protect themselves, some sellers write out the full term as "1000000".

With the aim of avoiding ambiguity the International Electrotechnical Commission (IEC) adopted new binary prefixes in 1998 (IEC 80000-13:2008 formerly subclauses 3.8 and 3.9 of IEC 60027-2:2005) Each binary prefix is formed from the first syllable of the decimal prefix with the similar value, and the syllable "bi". The symbols are the decimal symbol, always capitalised, followed by the letter "i". According to these standards, kilo, mega, giga et seq. should only be used in the decimal sense, even when referring to data storage capacities: kilobyte and megabyte denote one thousand and one million bytes respectively (consistent with the metric system), while terms such as kibibyte, mebibyte and gibibyte, with symbols KiB, MiB and GiB, denote 210, 220 and 230 bytes respectively.[10]

## Unofficial prefixes

A metric prefix myria-, abbreviation my-, for 10,000, was deprecated in 1960. Many personal, and sometimes facetious, proposals for additional metric prefixes have been formulated.[11][12] The prefix bronto, as used in the term brontobyte, has been used to represent anything from 1015 to 1027 bytes, most often 1027.[13][14][15][16][17] In 2010, an online petition sought to establish hella as the SI prefix for 1027, a movement that began on the campus of UC Davis.[18][19] The prefix, which has since appeared in the San Francisco Chronicle, Daily Telegraph, Wired and some other scientific magazines, was recognised by Google, in a non-serious fashion, in May 2010.[20][21][22] Ian Mills, president of the Consultative Committee on Units, considers the chances of official adoption to be remote.[23] The prefix geop and term geopbyte has been used in the tech industry to refer to 1030 bytes following brontobyte.[13]

The ascending prefixes peta (10005) and exa (10006) are based on the Greek-derived numeric prefixes penta (5) and hexa (6). The largest prefixes zetta (10007), and yotta (10008) and, similarly, the descending prefixes zepto (1000−7) and yocto (1000−8) are derived from Latin[24] septem (7) and octo (8) plus the initial letters z and y. The initial letters z and y, appear in the largest SI prefixes. They were changed because previously proposed ascending hepto (Greek hepta (7)) was already in use as a numerical prefix (implying seven) and the letter h as both SI-accepted non-SI unit (hour) and prefix (hecto 102), the same applied to s from previously proposed descending septo (i.e. SI unit s seconds), while o for octo was problematic since a symbol o could be confused with zero.[nb 1] A proposal made in 2019 to the BIPM is ronna (R) for 1027, quecca (Q) for 1030, ronto (r) for 10−27 and quecto (q) for 10−30.[25][26][27] A draft resolution by the BIPM revises this with quetta in place of quecca.[28]

Several personal proposals have been made for extending the series of prefixes, with ascending terms such as xenna, weka, vendeka (from Greek ennea (9), deka (10), endeka (11)) and descending terms such as xono, weco, vundo (from Latin novem/nona (9), decem (10), undecim (11). Using Greek for ascending and Latin for descending would be consistent with established prefixes such as deca, hecto, kilo vs. deci, centi, milli).[29] Although some of these are repeated on the internet, none are in actual use.[30]

## Notes

1. ^ "The names zepto and zetta suggest the digit seven [sept] (seventh power of 103) and the letter 'z' replaces the letter 's' to avoid the duplicate use of the letter 's' as a symbol. The names yocto and yotta are derived from octo, which suggests the number eight (eighth power of 103); the letter 'y' is added to avoid the use of the letter 'o' as a symbol because of the possible confusion with the digit zero." resolution 4 – BIPM

## References

1. ^ "Four Resolutions". Bipm.org. Retrieved 2012-03-01.
2. ^ 29th Congress of the United States, Session 1 (1866-05-13). "H.R. 596, An Act to authorise the use of the metric system of weights and measures". Archived from the original on 2013-05-10.
3. ^ a b Brewster, David (1830). The Edinburgh Encyclopædia. Vol. 12. Edinburgh, UK: William Blackwood, John Waugh, John Murray, Baldwin & Cradock, J. M. Richardson. p. 494. Retrieved 2015-10-09.
4. ^ a b Brewster, David (1832). The Edinburgh Encyclopaedia. Vol. 12 (1st American ed.). Joseph and Edward Parker. Retrieved 2015-10-09.
5. ^ histoire.du.metre.free.fr
6. ^ Dingler, Johann Gottfried (1823). Polytechnisches Journal (in German). Vol. 11. Stuttgart, Germany: J.W. Gotta'schen Buchhandlung. Retrieved 2015-10-09.
7. ^ Shrivatav, P. N., ed. (1971). "Appendix B - XII Conversion Table". Gazetteer of India: Madhya Pradesh District Gazetteers - Indore. District Gazetteers Department, Madhya Pradesh, Bhopal. p. 785.
8. ^ Reimer, Jeremy (2006-06-30). "Western Digital settles drive size lawsuit". Ars Technica LLC. Retrieved 2012-02-18.
9. ^ Seagate lawsuit concludes, settlement announced, bit-tech.net
10. ^ "International System of Units (SI): Prefixes for binary multiples". The NIST Reference on Constants, Units, and Uncertainty. National Institute of Science and Technology. Retrieved 2007-09-09.
11. ^ Michon, Gerard P. "Current and Deprecated Prefixes".
12. ^ Foley, John. "Funny prefixes & dubious proposals (updated yearly)".
13. ^ a b Michon, Gerard P. "Extreme Big Data: Beyond Zettabytes And Yottabytes". Forbes.
14. ^ BBC article suggesting that a brontobyte is 1027 bytes
15. ^ Sybase article suggesting that a brontobyte is 1027 bytes
16. ^ Article suggesting that brontobyte is 1027 bytes
17. ^ "Article suggesting that a brontobyte is 1015 bytes". MacUser. 7: 362. 1991-02-16. 1 brontobyte (1,000,000,000 megabytes)
18. ^ "Hellabytes? A Campaign to Turn Slang into Science". Time. 2010-03-10. Archived from the original on March 13, 2010. Retrieved 2010-05-20.
19. ^ Moore, Matthew (2010-03-02). "Hella number: scientists call for new word for 1,000,000,000,000,000,000,000,000,000". The Telegraph. Retrieved 2019-01-04. More than 20,000 scientists, students and members of the public have signed an online petition backing the new quantity, which would be used for figures with 27 zeros after the first digit.
20. ^ "Jargon Watch". Wired. Vol. 18, no. 6. June 2010. […] a proposed metric prefix […] useful for describing mega-measurements like Earth's mass (6 Hellagrams). A Facebook petition garnered 30000 signatures
21. ^ "The Official Petition to Establish "Hella-" as the SI Prefix for 10^27". Facebook. Retrieved 2010-06-04.
22. ^ Kim, Ryan (2010-05-24). "Google gets behind 'hella' campaign". The San Francisco Chronicle. Retrieved 2010-06-04.
23. ^ Chawkins, Steve (2010-06-06). "Physics major has a name for a really big number". Los Angeles Times: 2.
24. ^ Proceedings of the 19th CGPM (1991), page 80.
25. ^ Adam, David (14 February 2019). "You know kilo, mega, and giga. Is the metric system ready for ronna and quecca?". Science. doi:10.1126/science.aax0020. S2CID 86492572.
26. ^ Richard J. C. Brown, Extending the available range of SI prefixes
27. ^ Brown, R. J. (2019), "On the nature of SI prefixes and the requirements for extending the available range", Measurement, 137: 339–343, Bibcode:2019Meas..137..339B, doi:10.1016/j.measurement.2019.01.059, S2CID 117531445
28. ^ Draft Resolutions of the General Conference for Weights and Measures, 27th meeting (15–18 November 2022), page 22. Retrieved 2022-02-16
29. ^ For example, "International System" in Glenn Elert, The Physics Hypertextbook
30. ^ "Large Numbers – Notes (page 3) at MROB".