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Numerals express numbers and their relations to other numbers. Examples of such relations are: quantity, sequence, frequency, and part (fraction).
Many words of different parts of speech indicate 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 (one would say the equivalent of "five of people"). In English grammar, the classification "numeral" (viewed as a part of speech) 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. (Note that *dozen dogs played in the park is not grammatical, so 'dozen' is not a numeral in this sense.) 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 (first, second, third, etc.; from 'third' up, these are also used for fractions), multiplicative numbers (once, twice, and thrice), multipliers (single, double, and triple), and distributive numbers (singly, doubly, and triply). Georgian, Latin, and Romanian (see Romanian distributive numbers) 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 (see Russian numerals, Polish numerals).
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 (such as Guarani), a numeral system has been invented internally rather than borrowed. Other languages had an indigenous system but borrowed a second set of numerals anyway. An example is Japanese, which uses either native or Chinese-derived numerals depending on what is being counted.
English has derived numerals for multiples of its base (fifty, sixty, etc), 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 (with a second word for 25 only found in a compound for 75), 35, 45, 50, 150, 175, 200 (with a second found in a compound for 1200), 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 (short scale) or of a million (long scale—see names of large numbers). These words cannot modify a noun without being preceded by an article or numeral (*hundred dogs played in the park), and so are nouns.
In East Asia, the higher units are hundred, thousand, myriad 104, and powers of myriad. In India, 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 (202), pik 8000 (203), kalab 160,000 (204), etc.
Numerals of cardinal numbers
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The cardinal numbers have numerals. In the following tables, [and] indicates that the word and is used in some dialects (such as British English), and omitted in other dialects (such as American English).
This table demonstrates the standard English construction of small cardinal numbers up to one hundred million—names for which all variants of English agree.
|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, Sunya (Sanskrit)|
|1||One||ace, individual, single, singleton, unary, unit, unity, Pratham(Sanskrit)|
|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, walking stick|
|8||Eight||octad, octave, octet, octonary, octuplet, ogdoad|
|10||Ten||deca, decade, das (India)|
|11||Eleven||onze, ounze, ounce, banker's dozen|
|13||Thirteen||baker's dozen, long dozen|
|21||Twenty-one||long score, blackjack|
|70||Seventy||three-score and ten|
|87||Eighty-seven||four-score and seven|
|90||Ninety||four-score and ten|
|100||One hundred||centred, century, ton, short hundred|
|111||One hundred [and] eleven||eleventy-one|
|120||One hundred [and] twenty||long hundred, great hundred, (obsolete) hundred|
|144||One hundred [and] forty-four||gross, dozen dozen, small gross|
|1000||One thousand||chiliad, grand, G, thou, yard, kilo, k, millennium, Hajaar (India)|
|1024||One thousand [and] twenty-four||kibi or kilo in computing, see binary prefix (kilo is shortened to K, Kibi to Ki)|
|1100||One thousand one hundred||Eleven hundred|
|1728||One thousand seven hundred [and] twenty-eight||great gross, long gross, dozen gross|
|10000||Ten thousand||myriad, wan (China)|
|100000||One hundred thousand||lakh|
|500000||Five hundred thousand||crore (Iranian)|
|1000000||One million||Mega, meg, mil, (often shortened to M)|
|1048576||One million forty-eight thousand five hundred [and] seventy-six||Mibi or Mega in computing, see binary prefix (Mega is shortened to M, Mibi to Mi)|
|10000000||Ten million||crore (Indian)(Pakistan)|
|100000000||One hundred million||yi (China)|
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.
|Short scale||Long scale|
|Continental European |
(Jacques Peletier du Mans)
The following table details the myriad, octad, 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. For instance, in this system, 1032 would be represented as 1'0000,0000;0000,0000:0000,0000;0000,0000.[clarification needed]
|Value||Myriad System Name||Octad System Name||Chinese Myriad Scale||Chinese Long Scale||Knuth-proposed|
|104||Myriad||Myriad||萬 (万)||萬 (万)||Myriad|
|105||Ten myriad||Ten myriad||十萬 (十万)||十萬 (十万)||Ten myriad|
|106||Hundred myriad||Hundred myriad||百萬 (百万)||百萬 (百万)||Hundred myriad|
|107||Thousand myriad||Thousand myriad||千萬 (千万)||千萬 (千万)||Ten hundred myriad|
|108||Second Myriad||Octad||億 (亿)||億 (亿)||Myllion|
|1012||Third myriad||Myriad Octad||兆||萬億||Myriad myllion|
|1016||Fourth myriad||Second octad||京||兆||Byllion|
|1020||Fifth myriad||Myriad second octad||垓||萬兆|
|1024||Sixth myriad||Third octad||秭||億兆||Myllion byllion|
|1028||Seventh myriad||Myriad third octad||穰||萬億兆|
|1032||Eighth myriad||Fourth octad||溝 (沟)||京||Tryllion|
|1036||Ninth myriad||Myriad fourth octad||澗 (涧)||萬京|
|1040||Tenth myriad||Fifth octad||正||億京|
|1044||Eleventh myriad||Myriad fifth octad||載 (载)||萬億京|
|1048||Twelveth myriad||Sixth octad||極 (极) (in China and in Japan)||兆京|
|1052||Thirteenth myriad||Myriad sixth octad||恆河沙 (恒河沙) (in China)||萬兆京|
|1056||Fourteenth myriad||Seventh octad||阿僧祇 (in China); 恆河沙 (恒河沙) (in Japan)||億兆京|
|1060||Fifteenth myriad||Myriad seventh octad||那由他, 那由多 (in China)||萬億兆京|
|1064||Sixteenth myriad||Eighth octad||不可思議 (不可思议) (in China), 阿僧祇 (in Japan)||垓||Quadyllion|
|1068||Seventeenth myriad||Myriad eighth octad||無量大数 (in China)||萬垓|
|1072||Eighteenth myriad||Nineth octad||那由他, 那由多 (in Japan)||億垓|
|1080||Twentieth myriad||Tenth octad||不可思議 (in Japan)||兆垓|
|1088||Twenty-second myriad||Eleventh Octad||無量大数 (in Japan)||億兆垓|
Numerals of Fractions
This is a table of English names for non-negative rational numbers less than or equal to 1. It also lists alternative names, but there is no widespread convention for the names of extremely small positive numbers.
Keep in mind that rational numbers like 0.12 can be represented in infinitely many ways, e.g. zero-point-one-two (0.12), twelve percent (12%), three twenty-fifths (3/), nine seventy-fifths (9/), six fiftieths (6/), twelve hundredths (12/), twenty-four two-hundredths (24/), etc.
|0.9||9/||Nine tenths, [zero] point nine|
|0.8||4/||Four fifths, eight tenths, [zero] point eight|
|0.75||3/||three quarters, three fourths, seventy-five hundredths, [zero] point seven five|
|0.7||7/||Seven tenths, [zero] point seven|
|0.6||3/||Three fifths, six tenths, [zero] point six|
|0.5||1/||One half, five tenths, [zero] point five|
|0.4||2/||Two fifths, four tenths, [zero] point four|
|0.3||3/||Three tenths, [zero] point three|
|0.25||1/||One quarter, one fourth, twenty-five hundredths, [zero] point two five|
|0.2||1/||One fifth, two tenths, [zero] point two|
|0.125||1/||One eighth, one-hundred-[and-]twenty-five thousandths, [zero] point one two five|
|0.1||1/||One tenth, [zero] point one, One perdecime, one perdime|
|0.09||9/||Nine hundredths, [zero] point zero nine|
|0.08||2/||Two twenty-fifths, eight hundredths, [zero] point zero eight|
|0.0625||1/||One sixteenth, six-hundred-[and-]twenty-five ten-thousandths, [zero] point zero six two five|
|0.05||1/||One twentieth, five hundredths, [zero] point zero five|
|0.04||1/||One twenty-fifth, four hundredths, [zero] point zero four|
|0.03125||1/||One thirty-second, thirty one-hundred [and] twenty five hundred-thousandths, [zero] point zero three one two five|
|0.03||3/||Three hundredths, [zero] point zero three|
|0.025||1/||One fortieth, twenty-five thousandths, [zero] point zero two five|
|0.02||1/||One fiftieth, two hundredths, [zero] point zero two|
|0.015625||1/||One sixty-fourth, ten thousand fifty six-hundred [and] twenty-five millionths, [zero] point zero one five six two five|
|0.01||1/||One hundredth, [zero] point zero one, One percent|
|0.008264462809917355371900...||1/||One over one hundred twenty-one|
|0.001||1/||One thousandth, [zero] point zero zero one, One permille|
|0.000277777...||1/||One thirty-six hundredth|
|0.0001||1/||One ten-thousandth, [zero] point zero zero zero one, One myriadth, one permyria, one permyriad, one basis point|
|0.00001||1/||One hundred-thousandth, [zero] point zero zero zero zero one, One lakhth, one perlakh|
|0.000001||1/||One millionth, [zero] point zero zero zero zero zero one, One ppm|
|0.0000001||1/||One ten-millionth, One crorth, one percrore|
|0.000000001||1/||One billionth (in some dialects), One ppb|
|0.000000000001||1/||One trillionth, One ppt|
Various terms have arisen to describe commonly used measured quantities.
- Pair: 2 (the base of the binary numeral system)
- Dozen: 12 (the base of the duodecimal numeral system)
- Baker's dozen: 13
- Score: 20 (the base of the vigesimal numeral system)
- Gross: 144 (= 122)
- Great gross: 1728 (= 123)
Numerals in various languages
A database Numeral Systems of the World's Languages compiled by Eugene S.L. Chan of Hong Kong is hosted by the Max Planck Institute for Evolutionary Anthropology in Leipzig, Germany. The database currently contains data for about 4000 languages.
- Proto-Indo-European numerals
- Proto-Semitic numerals
- Chinese numerals
- Australian Aboriginal enumeration
- Balinese numerals
- Dzongkha numerals
- Finnish numerals
- Javanese numerals
- Yoruba numerals
- Charles Follen: A Practical Grammar of the German Language. Boston, 1828, p. 9, p. 44 and 48. Quote: "PARTS OF SPEECH. There are ten parts of speech, viz. Article, Substantive or Noun, Adjective, Numeral, Pronoun, Verb, Adverb, Preposition, Conjunction, and Interjection.", "NUMERALS. The numbers are divided into cardinal, ordinal, proportional, distributive, and collective. [...] Numerals of proportion and distribution are [...] &c. Observation. The above numerals, in fach or fäl´tig, are regularly declined, like other adjectives."
- Horace Dalmolin: The New English Grammar: With Phonetics, Morphology and Syntax, Tate Publishing & Enterprises, 2009, p. 175 & p. 177. Quote: "76. The different types of words used to compose a sentence, in order to relate an idea or to convey a thought, are known as parts of speech. [...] The parts of speech, with a brief definition, will follow. [...] 87. Numeral: Numerals are words that express the idea of number. There are two types of numerals: cardinal and ordinal. The cardinal numbers (one, two, three...) are used for counting people, objects, etc. Ordinal numbers (first, second, third...) can indicate order, placement in rank, etc."
- "What is a numeral?".
- Blunt, Joseph (1 January 1837). "The Shipmaster's Assistant, and Commercial Digest: Containing Information Useful to Merchants, Owners, and Masters of Ships". E. & G.W. Blunt – via Google Books.
- Ezard, John (2 Jan 2003). "Tolkien catches up with his hobbit". The Guardian. Retrieved 6 Apr 2018.