Numeral (linguistics)

In linguistics, a numeral in the broadest sense is a word or phrase that describes a numerical quantity. Some theories of grammar use the word "numeral" to refer to cardinal numbers that act as a determiner that specify the quantity of a noun, for example the "two" in "two hats". Some theories of grammar do not include determiners as a part of speech and consider "two" in this example to be an adjective. Some theories consider "numeral" to be a synonym for "number" and assign all numbers to a part of speech called "numerals". Numerals in the broad sense can also be analyzed as a noun, as a pronoun, or for a small number of words as an adverb.
Numerals can express relationships like quantity, sequence, frequency, and part.

Identifying numerals

Numerals may be attributive, as in two dogs, or pronominal, as in I saw two .
Words across various parts of speech often denote number or quantity. Such words are called quantifiers. Examples are words such as every, most, least, some, etc. Numerals are distinguished from other quantifiers by the fact that they designate a specific number. Examples are words such as five, ten, fifty, one hundred, etc. They may or may not be treated as a distinct part of speech; this may vary, not only with the language, but with the choice of word. For example, "dozen" serves the function of a noun, "first" serves the function of an adjective, and "twice" serves the function of an adverb. In Old Church Slavonic, the cardinal numbers 5 to 10 were feminine nouns; when quantifying a noun, that noun was declined in the genitive plural like other nouns that followed a noun of quantity. In English grammar, the classification "numeral" is reserved for those words which have distinct grammatical behavior: when a numeral modifies a noun, it may replace the article: the/some dogs played in the park → twelve dogs played in the park. English numerals indicate cardinal numbers. However, not all words for cardinal numbers are necessarily numerals. For example, million is grammatically a noun, and must be preceded by an article or numeral itself.
Numerals may be simple, such as 'eleven', or compound, such as 'twenty-three'.
In linguistics, however, numerals are classified according to purpose: examples are ordinal numbers, multiplicative numbers, multipliers, and distributive numbers. Georgian, Latin, and Romanian have regular distributive numbers, such as Latin singuli "one-by-one", bini "in pairs, two-by-two", terni "three each", etc. In languages other than English, there may be other kinds of number words. For example, in Slavic languages there are collective numbers which describe sets, such as pair or dozen in English.
Some languages have a very limited set of numerals, and in some cases they arguably do not have any numerals at all, but instead use more generic quantifiers, such as 'pair' or 'many'. However, by now most such languages have borrowed the numeral system or part of the numeral system of a national or colonial language, though in a few cases, a numeral system has been invented internally rather than borrowed. Other languages had an indigenous system but borrowed a second set of numerals anyway. Two examples are Japanese and Korean, which use either native or Chinese-derived numerals depending on what is being counted.
In many languages, such as Chinese, numerals require the use of numeral classifiers. Many sign languages, such as ASL, incorporate numerals.

Larger numerals

English has derived numerals for multiples of its base, and some languages have simplex numerals for these, or even for numbers between the multiples of its base. Balinese, for example, currently has a decimal system, with words for 10, 100, and 1000, but has additional simplex numerals for 25, 35, 45, 50, 150, 175, 200, 400, 900, and 1600. In Hindustani, the numerals between 10 and 100 have developed to the extent that they need to be learned independently.
In many languages, numerals up to the base are a distinct part of speech, while the words for powers of the base belong to one of the other word classes. In English, these higher words are hundred 10², thousand 10³, million 10⁶, and higher powers of a thousand or of a million. These words cannot modify a noun without being preceded by an article or numeral, and so are nouns.
In East Asia, the higher units are hundred, thousand, myriad 10⁴, and powers of myriad. In the Indian subcontinent, they are hundred, thousand, lakh 10⁵, crore 10⁷, and so on. The Mesoamerican system, still used to some extent in Mayan languages, was based on powers of 20: bak’ 400, pik 8000, kalab 160,000, etc.

Numerals of cardinal numbers

The cardinal numbers have numerals. In the following tables, indicates that the word and is used in some dialects, and omitted in other dialects.
This table demonstrates the standard English construction of some cardinal numbers.

Value	Name	Alternate names, and names for sets of the given size
0	Zero	aught, cipher, cypher, donut, dot, duck, goose egg, love, nada, naught, nil, none, nought, nowt, null, ought, oh, squat, zed, zilch, zip, zippo
1	One	ace, individual, single, singleton, unary, unit, unity
2	Two	binary, brace, couple, couplet, distich, deuce, double, doubleton, duad, duality, duet, duo, dyad, pair, span, twain, twin, twosome, yoke
3	Three	deuce-ace, leash, set, tercet, ternary, ternion, terzetto, threesome, tierce, trey, triad, trine, trinity, trio, triplet, troika, hat-trick
4	Four	foursome, quadruplet, quatern, quaternary, quaternity, quartet, tetrad
5	Five	cinque, fin, fivesome, pentad, quint, quintet, quintuplet
6	Six	half dozen, hexad, sestet, sextet, sextuplet, sise
7	Seven	heptad, septet, septuple
8	Eight	octad, octave, octet, octonary, octuplet, ogdoad
9	Nine	ennead
10	Ten	deca, decade, das
11	Eleven	onze, ounze, ounce, banker's dozen
12	Twelve	dozen
13	Thirteen	baker's dozen, long dozen
20	Twenty	score,
21	Twenty-one	long score, blackjack
22	Twenty-two	Deuce-deuce
24	Twenty-four	two dozen
40	Forty	two-score
50	Fifty	half-century
55	Fifty-five	double nickel
60	Sixty	three-score
70	Seventy	three-score and ten
80	Eighty	four-score
87	Eighty-seven	four-score and seven
90	Ninety	four-score and ten
100	One hundred	centred, century, ton, short hundred
111	One hundred eleven	eleventy-one
120	One hundred twenty	long hundred, great hundred, hundred
144	One hundred forty-four	gross, dozen dozen, small gross
1000	One thousand	chiliad, grand, G, thou, yard, kilo, k, millennium, Hajaar, ten hundred
1024	One thousand twenty-four	kibi or kilo in computing, see binary prefix
1100	One thousand one hundred	Eleven hundred
1728	One thousand seven hundred twenty-eight	great gross, long gross, dozen gross
10000	Ten thousand	myriad, wan
100000	One hundred thousand	lakh
500000	Five hundred thousand	crore
1000000	One million	Mega, meg, mil,
1048576	One million forty-eight thousand five hundred seventy-six	Mibi or Mega in computing, see binary prefix
10000000	Ten million	crore
100000000	One hundred million	yi

English names for powers of 10

This table compares the English names of cardinal numbers according to various American, British, and Continental European conventions. See English numerals or names of large numbers for more information on naming numbers.
There is no consistent and widely accepted way to extend cardinals beyond centillion.

Myriad, Octad, and [-yllion] systems

The following table details the myriad, octad, Ancient Greek Archimedes's notation, Chinese myriad, Chinese long and -yllion names for powers of 10.
There is also a Knuth-proposed system notation of numbers, named the -yllion system. In this system, a new word is invented for every 2ⁿ-th power of ten.

Value	Myriad System Name	Octad System Name	Ancient Greek Myriad Scale	Chinese Myriad Scale	Chinese Long Scale	Knuth-proposed System Name
10⁰	One	One	εἷς	一	一	One
10¹	Ten	Ten	δέκα	十	十	Ten
10²	Hundred	Hundred	ἑκατόν	百	百	Hundred
10³	Thousand	Thousand	χίλιοι	千	千	Ten hundred
10⁴	Myriad	Myriad	μύριοι	萬	萬	Myriad
10⁵	Ten myriad	Ten myriad	δεκάκις μύριοι	十萬	十萬	Ten myriad
10⁶	Hundred myriad	Hundred myriad	ἑκατοντάκις μύριοι	百萬	百萬	Hundred myriad
10⁷	Thousand myriad	Thousand myriad	χιλιάκις μύριοι	千萬	千萬	Ten hundred myriad
10⁸	Second myriad	Octad	μυριάκις μύριοι	億	億	Myllion
10⁹	Ten second myriad	Ten octad	δεκάκις μυριάκις μύριοι	十億	十億	Ten myllion
10¹⁰	Hundred second myriad	Hundred octad	ἑκατοντάκις μυριάκις μύριοι	百億	百億	Hundred myllion
10¹¹	Thousand second myriad	Thousand octad	χῑλῐάκῐς μυριάκις μύριοι	千億	千億	Ten hundred myllion
10¹²	Third myriad	Myriad octad	μυριάκις μυριάκις μύριοι	兆	萬億	Myriad myllion
10¹³	Ten third myriad	Ten myriad octad	δεκάκις μυριάκις μυριάκις μύριοι	十兆	十萬億	Ten myriad myllion
10¹⁴	Hundred third myriad	Hundred myriad octad	ἑκατοντάκις μυριάκις μυριάκις μύριοι	百兆	百萬億	Hundred myriad myllion
10¹⁵	Thousand third myriad	Thousand myriad octad	χιλιάκις μυριάκις μυριάκις μύριοι	千兆	千萬億	Ten hundred myriad myllion
10¹⁶	Fourth myriad	Second octad	μυριάκις μυριάκις μυριάκις μύριοι	京	兆	Byllion
10¹⁷	Ten fourth myriad	Ten second octad	δεκάκις μυριάκις μυριάκις μυριάκις μύριοι	十京	十兆	Ten byllion
10¹⁸	Hundred fourth myriad	Hundred second octad	ἑκατοντάκις μυριάκις μυριάκις μυριάκις μύριοι	百京	百兆	Hundred byllion
10¹⁹	Thousand fourth myriad	Thousand second octad	χιλιάκις μυριάκις μυριάκις μυριάκις μύριοι	千京	千兆	Ten hundred byllion
10²⁰	Fifth myriad	Myriad second octad	μυριάκις μυριάκις μυριάκις μυριάκις μύριοι	垓	萬兆	Myriad byllion
10²¹	Ten fifth myriad	Ten myriad second octad	δεκάκις μυριάκις μυριάκις μυριάκις μυριάκις μύριοι	十垓	十萬兆	Ten myriad byllion
10²²	Hundred fifth myriad	Hundred myriad second octad	ἑκατοντάκις μυριάκις μυριάκις μυριάκις μυριάκις μύριοι	百垓	百萬兆	Hundred myriad byllion
10²³	Thousand fifth myriad	Thousand myriad second octad	χιλιάκις μυριάκις μυριάκις μυριάκις μυριάκις μύριοι	千垓	千萬兆	Ten hundred myriad byllion
10²⁴	Sixth myriad	Third octad	μυριάκις μυριάκις μυριάκις μυριάκις μυριάκις μύριοι	秭 ; ?	億兆	Myllion byllion
10²⁸	Seventh myriad	Myriad third octad		穰	萬億兆	Myriad myllion byllion
10³²	Eighth myriad	Fourth octad		溝	京	Tryllion
10³⁶	Ninth myriad	Myriad fourth octad		澗	萬京	Myriad tryllion
10⁴⁰	Tenth myriad	Fifth octad		正	億京	Myllion tryllion
10⁴⁴	Eleventh myriad	Myriad fifth octad		載	萬億京	Myriad myllion tryllion
10⁴⁸	Twelfth myriad	Sixth octad		極	兆京	Byllion tryllion
10⁵²	Thirteenth myriad	Myriad sixth octad		恆河沙	萬兆京	Myriad byllion tryllion
10⁵⁶	Fourteenth myriad	Seventh octad		阿僧祇 ; 恒河沙	億兆京	Myllion byllion tryllion
10⁶⁰	Fifteenth myriad	Myriad seventh octad		那由他, 那由多	萬億兆京	Myriad myllion byllion tryllion
10⁶⁴	Sixteenth myriad	Eighth octad		不可思議 , 阿僧祇	垓	Quadyllion
10⁶⁸	Seventeenth myriad	Myriad eighth octad		無量大數	萬垓	Myriad quadyllion
10⁷²	Eighteenth myriad	Ninth octad		那由他, 那由多	億垓	Myllion quadyllion
10⁸⁰	Twentieth myriad	Tenth octad		不可思議	兆垓	Byllion quadyllion
10⁸⁸	Twenty-second myriad	Eleventh octad		無量大数	億兆垓	Myllion byllion quadyllion
10¹²⁸	Thirty-second myriad	Sixteenth octad			秭	Quinyllion
10²⁵⁶	Sixty-fourth myriad	Thirty-second octad			穰	Sexyllion
10⁵¹²	128th myriad	Sixty-fourth octad			溝	Septyllion
10^1,024	256th myriad	128th octad			澗	Octyllion
10^2,048	512th myriad	256th octad			正	Nonyllion
10^4,096	1024th myriad	512th octad			載	Decyllion
10^8,192	2048th myriad	1024th octad			極	Undecyllion
10^16,384	4096th myriad	2048th octad			恆河沙	Duodecyllion
10^32,768	8192nd myriad	4096th octad			阿僧祇	Tredecyllion
10^65,536	16384th myriad	8192nd octad			那由他, 那由多	Quattuordecyllion
10^131,072	32768th myriad	16384th octad			不可思議	Quindecyllion
10^262,144	65536th myriad	32768th octad			無量大數	Sexdecyllion
10^524,288	131072nd myriad	65536th octad				Septendecyllion
10^1,048,576	262144th myriad	131072nd octad				Octodecyllion
10^2,097,152	524288th myriad	262144th octad				Novemdecyllion
10^4,194,304	1048576th myriad	524288th octad				Vigintyllion
10^2³²	1073741824th myriad	536870912th octad				Trigintyllion
10^2⁴²	1099511627776th myriad	549755813888th octad				Quadragintyllion
10^2⁵²						Quinquagintyllion
10^2⁶²						Sexagintyllion
10^2⁷²						Septuagintyllion
10^2⁸²						Octogintyllion
10^2⁹²						Nonagintyllion
10^2¹⁰²						Centyllion
10^{2^1,002}						Millyllion
10^{2^10,002}						Myryllion