Unit prefix

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

Metric prefixes in everyday use
Text	Symbol	Factor	Power
exa	E	1000000000000000000	10^18
peta	P	1000000000000000	10^15
tera	T	1000000000000	10^12
giga	G	1000000000	10^9
mega	M	1000000	10^6
kilo	k	1000	10^3
hecto	h	100	10^2
deca	da	10	10^1
(none)	(none)	1	10^0
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
femto	f	0.000000000000001	10^−15
atto	a	0.000000000000000001	10^−18

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]

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. In mathematical contexts, the unit prefixes are always considered part of the unit, so that, e.g., in exponentiation, 1 km² means one square kilometre not one thousand square metre 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 a factors of 10000, 2 and  ¹⁄₂ 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 1000^2 M mega 1000^3 G giga 1000^4 T tera 1000^5 P peta 1000^6 E exa 1000^7 Z zetta 1000^8 Y yotta	Binary Value IEC JEDEC 1024 Ki kibi K kilo 1024^2 Mi mebi M mega 1024^3 Gi gibi G giga 1024^4 Ti tebi – 1024^5 Pi pebi – 1024^6 Ei exbi – 1024^7 Zi zebi – 1024^8 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. would only be used in the decimal sense, even when referring to data storage capacities: kilobyte and megabyte would denote one thousand and one million bytes respectively (consistent with the metric system), while new terms such as kibibyte, mebibyte and gibibyte, with symbols KiB, MiB and GiB, would denote 2¹⁰, 2²⁰ and 2³⁰ bytes respectively.^[10] The new prefixes have mainly been used in scientific or technical literature. Their adoption in popular publications remains limited.

Unofficial prefixes

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]} The SI includes standardised prefixes for 10¹⁵ (peta), 10¹⁸ (exa), 10²¹ (zetta) and 10²⁴ (yotta). 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), exa (1000⁶), zetta (1000⁷), and yotta (1000⁸) are based on the Greek-derived numeric prefixes penta (5), hexa (6), hepta (7), and octa or octo (8). In addition, the final letters of the alphabet, z and y, appear in the largest SI prefixes, zetta and yotta. Similarly, the descending prefixes zepto (1000⁻⁷) and yocto (1000⁻⁸) are derived from either Greek hepta and octo or Latin septem (7) and octo (8) plus the initial letters z and y. The initial letters were changed because s and h, from previously proposed ascending hepta and descending septo, were already used as SI units and prefixes (in German, septo would be pronounced as English zepto), and because the o of octa/octo could be confused with zero.^[24] The CGPM has decided to extend this z–y backwards through the alphabet,^[25] though it is not clear if the distinction of the historically related sets of letters u/v/w and i/j would be retained (it is common to avoid contrasting them in scientific series), or if letters such as S and T, which are already in use as SI units or prefixes, will again be skipped.^[26]

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), dec (10), undec (11). Using Greek for ascending and Latin for descending would be consistent with established prefixes such as deca, hecto, kilo vs deci, centi, milli).^[27] Although some of these are repeated on the internet, none are in actual use.^[28]

References

1. "Four Resolutions". Bipm.org. Retrieved 1 March 2012.
2. 29th Congress of the United States, Session 1 (13 May 1866). "H.R. 596, An Act to authorise the use of the metric system of weights and measures".
3. Brewster, David (1830). The Edinburgh Encyclopædia. 12. Edinburgh, UK: William Blackwood, John Waugh, John Murray, Baldwin & Cradock, J. M. Richardson. p. 494. Retrieved 2015-10-09.
4. Brewster, David (1832). The Edinburgh Encyclopaedia. 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). 11. Stuttgart, Germany: J.W. Gotta'schen Buchhandlung. Retrieved 2015-10-09.
7. PN Shrivatav, ed. (1971). "Appendix B - XII Conversion Table". Gazeteer of India: Madhya Pradesh District Gazeteers - Indore. District Gazeteers Department, Madhya Pradesh, Bhopal. p. 785.
8. Jeremy Reimer (30 June 2006). "Western Digital settles drive size lawsuit". Ars Technica LLC. Retrieved 18 February 2012.
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 9 September 2007.
11. Michon, Gerard P. "Current and Deprecated Prefixes".
12. Foley, John. "Funny prefixes & dubious proposals (updated yearly)".
13. Michon, Gerard P. "Extreme Big Data: Beyond Zettabytes And Yottabytes".
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. 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 2010-06-04. 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. 18 (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. p. 2.
24. "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."
25. SI prefixes for decimal multiples
26. Existing prefixes are a c d E f G h k M m n P T. Existing units are A C F g H J K l N S s T V W.
27. For example, "International System" in Glenn Elert, The Physics Hypertextbook

External links

• Moerner Lab Single-Molecule Research Page (Jokingly defines 1 guacamole = 1 / (Avocado's number) of moles. Scientific paper with reference)
• Vendeka.org Home page for the use of the non-SI prefix vendeka to represent 10 to the power of 33, as in vendekabyte.