Numeral prefix

Numeral or number prefixes are prefixes derived from numerals or occasionally other numbers. In English and other European languages, they are used to coin numerous series of words, such as unicycle – bicycle – tricycle, dyad – triad – decade, biped – quadruped, September – October – November – December, decimal – hexadecimal, sexagenarian – octogenarian, centipede – millipede, etc. There are two principal systems, taken from Latin and Greek, each with several subsystems; in addition, Sanskrit occupies a marginal position.^[1] There is also an international set of metric prefixes, which are used in the metric system, and which for the most part are either distorted from the forms below or not based on actual number words.

Table of number prefixes in English

In the following prefixes, a final vowel is normally dropped before a root that begins with a vowel, with the exceptions of bi-, which is bis- before a vowel, and of the other monosyllables, du-, di-, dvi-, tri-, which are invariable.

The cardinal series are derived from cardinal numbers, such as the English one, two, three. The multiple series are based on adverbial numbers like the English once, twice, thrice. The distributives originally meant one each, two each or one by one, two by two, etc., though that meaning is now frequently lost. The ordinal series is based on ordinal numbers such as the English first, second, third. For numbers higher than 2, the ordinal forms are also used for fractions; only the fraction ½ has special forms.

For the hundreds, there are competing forms: those in -gent-, from the original Latin, and those in -cent-, derived from centi- etc. plus the prefixes for 1–9.

Number	Latin prefixes				Greek prefixes		Sanskrit[1]
	Cardinal	Multiple	Distributive	Ordinal	Cardinal	Multiple
0	nulli-			–	–		–
^1⁄12	unci-			–	–		–
^1⁄8	octant-	–	–	–	–		–
^1⁄6	sextant-	–	–	–	–		–
^1⁄4	quadrant-	–	–	–	–		–
^1⁄3	trient-	–	–	–	–		–
^1⁄2	semi-	–	demi-[2]	–	hemi-	–	–
^3⁄4	dodrant-	–	–	–	–		–
1	uni-	sim-[3]	singul-	prim-	hen-[4]	mono-, haplo-[4]	eka-
1 ^1⁄4		quasqui-
1 ^1⁄2		sesqui-
2	du-	bi-, bis-	bin-	second-	di-, dy-, duo-	dis-, dyakis-	dvi-
3	tri-	ter-	tern-, trin-	terti-	tri-	tris-, triakis-	tri-
4	quadri-, quadru-[5]	quater-[6]	quatern-[7]	quart-[8]	tetra-	tetrakis-	chatur-
5	quinque-[9]	–	quin-[10]	quint-[11]	penta-	pentakis-	pancha-
6	sexa-[12]	–	sen-[13]	sext-[14]	hexa-	hexakis-	shat-
7	septem-, septi-		septen-[15]	septim-	hepta-	heptakis-	sapta-
8	octo-	–	octon-[16]	octav-[17]	ogdo-, octa-, octo-	octakis-	ashta-
9	novem-		noven-	nona-	ennea-	enneakis-	navam-
10	decem-, dec-		den-[18]	decim-[19]	deca-	decakis-	dasham-
11	undec-		unden-[20]	undecim-[21]	hendeca-	hendecakis-	ekadasham-
12	duodec-		duoden-	duodecim-	dodeca-	dodecakis-	dvadasham-
13	tredec-		treden-	tredecim-	tri(skai)deca-	tri(skai)decakis-	trayodasham-
14	quattuordec-		quattuorden-	quattuordecim-	tetra(kai)deca-	tetra(kai)decakis-	chaturdasham-
15	quinquadec-, quindec-[22]		quinden-[23]	quindecim-[24]	penta(kai)deca-, pente(kai)deca-	penta(kai)decakis-, pente(kai)decakis-	panchadasham-
16	sedec-,[25] sexdec- (but hybrid hexadecimal[12])		seden-	sedecim-	hexa(kai)deca-, hekkaideca-	hexa(kai)decakis-	shodasham-
17	septendec-		septenden-	septendecim-	hepta(kai)deca-	hepta(kai)decakis-	saptadasham-
18	octodec-		octoden-	octodecim-	octo(kai)deca-, octa(kai)deca-	octo(kai)decakis- octa(kai)decakis-	ashtadasham-
19	novemdec-, novendec-		novemden-	novemdecim-	ennea(kai)deca-	ennea(kai)decakis-	navadasham-
20*	viginti-		vicen-, vigen-	vigesim-	icosa-, icosi-, eicosa-	eicosakis-	vimshati-
24					icositetra-, icosikaitetra-, tetracosa-		chaturvimshati-
30	triginti-		tricen-	trigesim-	triaconta-	triacontakis-	trimshat-
40	quadraginti-		quadragen-	quadragesim-	tetraconta-	tetracontakis-	chatvarimshat-
50	quinquaginti-[26]		quinquagen-[27]	quinquagesim-[28]	pentaconta-, penteconta-	pentecontakis-	panchashat-
60	sexaginti-		sexagen-	sexagesim-	hexaconta-, hexeconta-	hexecontakis-	shasti-
70	septuaginti-		septuagen-	septuagesima-	heptaconta-, hebdomeconta-	hebdomecontakis-	saptati-
80	octogint-		octogen-	octogesim-	octaconta-, ogdoëconta-	ogdoëcontakis-	ashiti-
90	nonagint-		nonagen-	nonagesim-	enneaconta-, eneneconta-, enneneconta-	enneacontakis-	navati-
100	centi-		centen-	centesim-	hecato-, hecatont-	hecatontakis-	shata–
120					hecatonicosa-, dodecaconta-
200	ducenti-		ducen-, bicenten-	ducentesim-	diacosioi-	diacosakis-	–
300	trecenti-		trecen-, tercenten-, tricenten-	trecentesim-	triacosioi-	triacosakis-	–
400	quadringenti-		quadringen-, quatercenten-, quadricenten-	quadringentesim-	tetracosioi-	tetracosakis-
500	quingent-,[29] quincent-[30]		quingen-,[31] quingenten-, quincenten-	quingentesim-[32]	pentacosioi-	pentacosakis-
600	sescenti-, sexcenti-		sescen-, sexcenten-	sescentesim-	hexacosioi-	hexacosakis-
700	septingenti-		septingen-, septingenten-, septcenten-	septingentesim-	heptacosioi-	heptacosakis-
800	octingenti-		octingen-, octingenten-, octocenten-	octingentesim-	octacosioi-	octacosakis-	–
900	nongenti-		nongen-	nongentesim-	enneacosioi-, enacosioi-	enneacosakis-	–
1000	milli-		millen-	millesim-	chilia-	chiliakis-	sahasra–
10000	–				myria-	myriakis-	ayuta–
Unspecified (more than one)	multi-			–	poly-		bahu–

Sesqui- is used in Latin combinations for 1 ¹⁄₂ (e.g. sesquicentennial) and quasqui- for 1 ¹⁄₄; multi- and poly- are used in Latin and Greek combinations, respectively, for 'many' (multilateral, polygon).

*For Latinate 21, 22, etc., the pattern for the teens is followed: unvigint-, duovigint-, etc. For higher numbers, the reverse order may be found: 36 trigintisex-. For Greek, the word kai ('and') is used: icosikaihena-, icosikaidi-, pentacontakaipenta-, etc. In these and in the tens, the kai is frequently omitted, though not in triskaidekaphobia. (The inconsistency of triskaidekaphobia with the table above is explained by the fact that the Greek letter kappa can be transliterated either "c" or "k".)

The same suffix may be used with more than one series:

primary	secondary	tertiary	quartary	quintary	sextary	—	—	nonary	—
singulary	binary	ternary, trinary	quaternary	quinary	senary	septenary	octonary	novenary	denary

In chemical nomenclature, 11 is generally mixed Latin-Greek undeca-, and the 20s are based on -cos-, for example tricos- for 23. Similarly, numerical bases shift systems between binary, trinary, senary and octal, decimal, vigesimal.

Occurrences

• Numerical prefixes occur in 19th-, 20th-, and 21st-century coinages, mainly the terms that are used in relation to or that are the names of technological innovations, such as hexadecimal and bicycle. Also used in medals that commemorate an anniversary, such as sesquicentennial (150 years), centennial (100 years), or bicentennial (200 years).
• They occur in constructed words such as systematic names. Systematic names use numerical prefixes derived from Greek, with one principal exception, nona-.
• They occur as prefixes to units of measure in the SI system. See SI prefix.
• They occur as prefixes to units of computer data. See binary prefixes.
• They occur in words in the same languages as the original number word, and their respective derivatives. (Strictly speaking, some of the common citations of these occurrences are not in fact occurrences of the prefixes. For example: millennium is not formed from milli-, but is in fact derived from the same shared Latin root – mille.)

Because of the common inheritance of Greek and Latin roots across the Romance languages, the import of much of that derived vocabulary into non-Romance languages (such as into English via Norman French), and the borrowing of 19th and 20th century coinages into many languages, the same numerical prefixes occur in many languages.

Numerical prefixes are not restricted to denoting integers. Some of the SI prefixes denote negative powers of 10, i.e. division by a multiple of 10 rather than multiplication by it. Several common-use numerical prefixes denote vulgar fractions.

Words containing non-technical numerical prefixes are usually not hyphenated. This is not an absolute rule, however, and there are exceptions (for example: quarter-deck occurs in addition to quarterdeck). There are no exceptions for words comprising technical numerical prefixes, though. Systematic names and words comprising SI prefixes and binary prefixes are not hyphenated, by definition.

Nonetheless, for clarity, dictionaries list numerical prefixes in hyphenated form, to distinguish the prefixes from words with the same spellings (such as duo- and duo).

Several technical numerical prefixes are not derived from words for numbers. (mega- is not derived from a number word, for example.) Similarly, some are only derived from words for numbers inasmuch as they are word play. (Peta- is word play on penta-, for example. See its etymology for details.)

The root language of a numerical prefix need not be related to the root language of the word that it prefixes. Some words comprising numerical prefixes are hybrid words.

In certain classes of systematic names, there are a few other exceptions to the rule of using Greek-derived numerical prefixes. The IUPAC nomenclature of organic chemistry, for example, uses the numerical prefixes derived from Greek, except for the prefix for 9 (as mentioned) and the prefixes from 1 to 4 (meth-, eth-, prop-, and but-), which are not derived from words for numbers. These prefixes were invented by the IUPAC, deriving them from the pre-existing names for several compounds that it was intended to preserve in the new system: methane (via methyl which is in turn from the Greek word for wine), ethane (from ethyl coined by Justus von Liebig in 1834), propane (from propionic which is in turn from pro- and the Greek word for fat), and butane (from butyl which is in turn from butyric which is in turn from the Latin word for butter).

Cardinal Latin series

• unicycle, bicycle, tricycle, quadricycle
• uniped, biped, triped, quadruped,^[5] centipede, millipede

Distributive Latin series

• unary, binary, trinary, quaternary, quinary, senary, ... vicenary ... centenary ...
• quinquagenarian, sexagenarian, septuagenarian, octogenarian, nonagenarian, centenarian, ... millenarian

Greek series

• pentane, hexane, heptane, octane, nonane,^[33] decane, ... icosane
• monopod, bipod, tripod, tetrapod, hexapod, octopod, decapod
• monad, dyad, triad, tetrad, pentad, hexad, heptad, ogdoad, ennead, decad(e), ... triacontad, ... hecatontad, chiliad, myriad
• trilogy, tetralogy, pentalogy, hexalogy, heptalogy

See also

• List of numeral systems
• List of numbers in various languages
• List of commonly used taxonomic affixes

Notes

1. See Mendeleev's predicted elements for the most common use of Sanskrit numerical prefixes.
2. Demi- is actually French, from Latin dimidium.
3. Sim- (sin-) is found in the words simplex, simple.
4. The Greek prefix for 'one' is normally mono- 'alone'. Hen- 'one' is only used in compound numbers (hendeka- 11) and a few words like henad (= monad). Haplo- 'single' is found is a few technical words such as haploid.
5. The forms related to quattuor "four", like the previous three integers, are irregular in Latin and other Indo-European languages, and the details, while presumably a form of assimilation, are unclear. Andrew Sihler, New comparative grammar of Greek and Latin, p. 412, and Carl Darling Buck, Comparative grammar of Greek and Latin. In particular, quadri- has the alternate form quadru- before p in some Latin words, such as quadruple.
6. "quăter". Retrieved 2011-05-14.
7. "quăterni". Retrieved 2011-05-14.
8. "quartus". Retrieved 2011-05-14.
9. "quinque". Retrieved 2011-05-14.
10. "quīni". Retrieved 2011-05-14.
11. "quintus". Retrieved 2011-05-14.
12. Sometimes Greek hexa- is used in Latin compounds, such as hexadecimal, due to taboo avoidance with the English word sex.
13. "sēni". Retrieved 2011-05-14.
14. "sextus". Retrieved 2011-05-14.
15. "septēni". Retrieved 2011-05-14.
16. "octōni". Retrieved 2011-05-14.
17. "octāvus". Retrieved 2011-05-14.
18. "dēni". Retrieved 2011-05-14.
19. "dĕcĭmus". Retrieved 2011-05-14.
20. "undēni". Retrieved 2011-05-14.
21. "undĕcĭmus". Retrieved 2011-05-14.
22. "quindĕcim". Retrieved 2011-05-14.
23. "quindēni". Retrieved 2011-05-14.
24. "quindĕcĭmus". Retrieved 2011-05-14.
25. "sēdĕcim". Retrieved 2011-05-14.
26. "quinquāginta". Retrieved 2011-05-14.
27. "quinquāgēni". Retrieved 2011-05-14.
28. "quinquāgēsĭmus". Retrieved 2011-05-14.
29. "quingenti". Retrieved 2011-05-14.
30. "quincenti". Retrieved 2011-05-14.
31. "quingēni". Retrieved 2011-05-14.
32. "quingentēsĭmus". Retrieved 2011-05-14.
33. In organic chemistry, the prefix for 9 is Latin rather than Greek

References

• Oxford English Dictionary, 2nd edition
• Buck, Carl Darling, Comparative Grammar of Greek and Latin
• Sihler, Andrew Littleton, A New Comparative Grammar of Greek and Latin, Oxford University Press 1995 ISBN 0195083458

Further reading

• Stephen Chrisomalis. "Numerical Adjectives, Greek and Latin Number Prefixes". The Phrontistery.
• Christine Bauer-Ramazani (April 2008). "Prefixes--Amount, Relationship, Judgment, Other Prefixes".