Word or phrase which describes a numerical quantity
This article is about number words. For the mathematical notation of numbers, seenumeral system.
In linguistics, anumeral in the broadest sense is aword orphrase that describes a numericalquantity. Some theories ofgrammar use the word "numeral" to refer tocardinal numbers that act as adeterminer that specify the quantity of anoun, 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 anadjective. Some theories consider "numeral" to be asynonym for "number" and assign all numbers (includingordinal numbers like "first") to apart of speech called "numerals".[1][2] Numerals in the broad sense can also be analyzed as a noun ("three is a small number"), as apronoun ("the two went to town"), or for a small number of words as anadverb ("I rode the slide twice").
Numerals can express relationships like quantity (cardinal numbers),sequence (ordinal numbers),frequency (once, twice), and part (fraction).[3]
Words across various parts of speech often denote number or quantity. Such words are calledquantifiers. Examples are words such asevery,most,least,some, etc. Numerals are distinguished from other quantifiers by the fact that they designate a specific number.[3] Examples are words such asfive, 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 anoun, "first" serves the function of anadjective, and "twice" serves the function of anadverb. InOld Church Slavonic, the cardinal numbers 5 to 10 were feminine nouns; when quantifying a noun, that noun wasdeclined in the genitive plural like other nouns that followed a noun of quantity (one would say the equivalent of "fiveof people"). In English grammar, the classification "numeral" (viewed as apart of speech)[citation needed] is reserved for those words which have distinct grammatical behavior: when a numeral modifies a noun, it may replace thearticle:the/some dogs played in the park →twelve dogs played in the park. (*dozen dogs played in the park is not grammatical, so "dozen" is not a numeral in this sense.) English numerals indicatecardinal 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 areordinal numbers (first,second,third, etc.; from 'third' up, these are also used forfractional numerals in English, but other languages distinguish the two completely),multiplicative (adverbial) numbers (once,twice, andthrice),multipliers (single,double, andtriple), anddistributive numbers (singly,doubly, andtriply).Georgian,[4] Latin, and Romanian (seeRomanian distributive numbers) have regulardistributive numbers, such as Latinsinguli "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 arecollective numbers (monad, pair/dyad, triad) which describe sets, such aspair ordozen in English (seeRussian 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 asGuarani[5]), 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 areJapanese andKorean, which use 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. InHindustani, 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 distinctpart of speech, while the words for powers of the base belong to one of the other word classes. In English, these higher words arehundred 102,thousand 103,million 106, and higher powers of a thousand (short scale) or of a million (long scale—seenames 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.
This table compares the English names of cardinal numbers according to various American, British, and Continental European conventions. SeeEnglish numerals ornames of large numbers for more information on naming numbers.
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 aKnuth-proposed system notation of numbers, named the -yllion system.[8] In this system, a new word is invented for every2n-th power of ten.
This is a table of English names for non-negativerational 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 ininfinitely many ways, e.g.zero-point-one-two (0.12),twelvepercent (12%),three twenty-fifths (3/25),nine seventy-fifths (9/75),six fiftieths (6/50),twelve hundredths (12/100),twenty-four two-hundredths (24/200), etc.
Value
Fraction
Common names
1
1/1
One, Unity, Whole
0.9
9/10
Nine tenths, [zero] point nine
0.833333...
5/6
Five sixths
0.8
4/5
Four fifths, eight tenths, [zero] point eight
0.75
3/4
three quarters, three fourths, seventy-five hundredths, [zero] point seven five
Not all peoples usecounting, at least not verbally. Specifically, there is not much need for counting among hunter-gatherers who do not engage in commerce. Many languages around the world have no numerals above two to four (if they are actually numerals at all, and not some other part of speech)—or at least did not before contact with the colonial societies—and speakers of these languages may have no tradition of using the numerals they did have for counting. Indeed, several languages from the Amazon have been independently reported to have no specific number words other than 'one'. These includeNadëb, pre-contactMocoví andPilagá,Culina and pre-contactJarawara,Jabutí,Canela-Krahô,Botocudo (Krenák),Chiquitano, theCampa languages,Arabela, andAchuar.[10] Some languages of Australia, such asWarlpiri, do not have words for quantities above two,[11][12][13] and neither did manyKhoisan languages at the time of European contact. Such languages do not have a word class of 'numeral'.
Most languages with both numerals and counting use base 8, 10, 12, or 20. Base 10 appears to come from counting one's fingers, base 20 from the fingers and toes, base 8 from counting the spaces between the fingers (attested in California), and base 12 from counting the knuckles (3 each for the four fingers).[14]
Many languages ofMelanesia have (or once had) counting systems based on parts of the body which do not have a numeric base; there are (or were) no numerals, but rather nouns for relevant parts of the body—or simply pointing to the relevant spots—were used for quantities. For example, 1–4 may be the fingers, 5 'thumb', 6 'wrist', 7 'elbow', 8 'shoulder', etc., across the body and down the other arm, so that the opposite little finger represents a number between 17 (Torres Islands) to 23 (Eleman). For numbers beyond this, the torso, legs and toes may be used, or one might count back up the other arm and back down the first, depending on the people.[citation needed]
Binary systems are based on the number 2, using zeros and ones. Due to its simplicity, only having two distinct digits, binary is commonly used in computing, with zero and one often corresponding to "off/on" respectively.
Ternary systems are based on the number 3, having practical usage in some analog logic, in baseball scoring and inself–similar mathematical structures.
Quaternary systems are based on the number 4. SomeAustronesian,Melanesian,Sulawesi, andPapua New Guinea ethnic groups, count with the base number four, using the termasu oraso, the word fordog, as the ubiquitous village dog has four legs.[15] This is argued by anthropologists to be also based on early humans noting the human and animal shared body feature of two arms and two legs as well as its ease in simple arithmetic and counting. As an example of the system's ease a realistic scenario could include a farmer returning from the market with fiftyasu heads of pig (200), less 30asu (120) of pig bartered for 10asu (40) of goats noting his new pig count total as twentyasu: 80 pigs remaining. The system has a correlation to thedozen counting system and is still in common use in these areas as a natural and easy method of simple arithmetic.[15][16]
Quinary systems are based on the number 5. It is almost certain the quinary system developed from counting by fingers (five fingers per hand).[17] An example are theEpi languages of Vanuatu, where 5 isluna 'hand', 10lua-luna 'two hand', 15tolu-luna 'three hand', etc. 11 is thenlua-luna tai 'two-hand one', and 17tolu-luna lua 'three-hand two'.
5 is a commonauxiliary base, orsub-base, where 6 is 'five and one', 7 'five and two', etc.Aztec was a vigesimal (base-20) system with sub-base 5.
Senary systems are based on the number 6. The Morehead-Maro languages of Southern New Guinea are examples of the rare base 6 system with monomorphemic words running up to 66. Examples areKanum andKómnzo. TheSko languages on the North Coast of New Guinea follow a base-24 system with a sub-base of 6.
Septenary systems are based on the number 7. Septenary systems are very rare, as few natural objects consistently have seven distinctive features. Traditionally, it occurs in week-related timing. It has been suggested that thePalikúr language has a base-seven system, but this is dubious.[18]
Octal systems are based on the number 8. Examples can be found in theYuki language ofCalifornia and in thePamean languages ofMexico, because theYuki andPame keep count by using the four spaces between their fingers rather than the fingers themselves.[19]
Decimal systems are based on the number 10. A majority of traditional number systems are decimal. This dates back at least to the ancientEgyptians, who used a wholly decimal system. Anthropologists hypothesize this may be due to humans having fivedigits per hand, ten in total.[17][20] There are many regional variations including:
Duodecimal numeric systems have some practical advantages over decimal. It is much easier to divide the base digittwelve (which is ahighly composite number) by many importantdivisors inmarket and trade settings, such as the numbers2,3,4 and6.
Because of several measurements based on twelve,[21] many Western languages have words for base-twelve units such asdozen,gross andgreat gross, which allow for rudimentary duodecimalnomenclature, such as "two gross six dozen" for 360.Ancient Romans used a decimal system forintegers, but switched toduodecimal forfractions, and correspondinglyLatin developed a rich vocabulary for duodecimal-based fractions (seeRoman numerals). A notable fictional duodecimal system was that ofJ. R. R. Tolkien'sElvish languages, which used duodecimal as well as decimal.
The traditionalChinese units of measurement were base-16. For example, one jīn (斤) in the old system equals sixteentaels. Thesuanpan (Chineseabacus) can be used to perform hexadecimal calculations such as additions and subtractions.[22]
South Asian monetary systems were base-16. One rupee in Pakistan and India was divided into 16 annay. A singleanna was subdivided into fourpaisa or twelvepies (thus there were 64 paise or 192 pies in a rupee). The anna wasdemonetised as a currency unit when Indiadecimalised its currency in 1957, followed by Pakistan in 1961.
Vigesimal systems are based on the number 20. Anthropologists are convinced the system originated from digit counting, as did bases five and ten, twenty being the number of human fingers and toes combined.[17][23]The system is in widespread use across the world. Some include the classicalMesoamerican cultures, still in use today in the modern indigenous languages of their descendants, namely theNahuatl andMayan languages (seeMaya numerals). A modern national language which uses a full vigesimal system isDzongkha in Bhutan.
Partial vigesimal systems are found in some languages:Basque,Celtic languages,French (from Celtic),Danish, andGeorgian. In these languages the systems are vigesimal up to 99, then decimal from 100 up. That is, 140 is 'one hundred two score', not *seven score, and there is no numeral for 400 (great score).
The termscore originates fromtally sticks, and is perhaps a remnant of Celtic vigesimal counting. It was widely used to learn the pre-decimal British currency in this idiom: "a dozen pence and ascore ofbob", referring to the 20shillings in apound. For Americans the term is most known from the opening of theGettysburg Address:"Four score and seven years ago our fathers...".
Sexagesimal systems are based on the number 60.Ekari has a base-60 system.Sumeria had a base-60 system with a decimal sub-base (with alternating cycles of 10 and 6), which was the origin of the numbering of moderndegrees, minutes, and seconds.
Octogesimal systems are based on the number 80.Supyire is said to have a base-80 system; it counts in twenties (with 5 and 10 as sub-bases) up to 80, then by eighties up to 400, and then by 400s (great scores).
kàmpwóò
four hundred
ŋ̀kwuu
eighty
sicyɛɛré
four
ná
and
béé-tàànre
twenty-three
ná
and
kɛ́
ten
ná
and
báár-ìcyɛ̀ɛ̀rè
five-four
kàmpwóò ŋ̀kwuu sicyɛɛré ná béé-tàànre ná kɛ́ ná báár-ìcyɛ̀ɛ̀rè
{four hundred} eighty four and twenty-three and ten and five-four
799 [i.e. 400 + (4 x 80) + (3 x 20) + {10 + (5 + 4)}]’
^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 andordinal. The cardinal numbers (one, two, three...) are used for counting people, objects, etc. Ordinal numbers (first, second, third...) can indicateorder, placement inrank, etc."
^Cardarelli, François (2012).Encyclopaedia of Scientific Units, Weights and Measures: Their SI Equivalences and Origins (Second ed.). Springer. p. 585.ISBN978-1447100034.
^abRyan, Peter.Encyclopaedia of Papua and New Guinea. Melbourne University Press & University of Papua and New Guinea,:1972ISBN0-522-84025-6.: 3 pages p 219.
^Aleksandr Romanovich Luriicac, Lev Semenovich Vygotskiĭ, Evelyn Rossiter.Ape, primitive man, and child: essays in the history of behavior. CRC Press: 1992:ISBN1-878205-43-9.
