Word or phrase which describes a numerical quantity
This article is about number words. For the mathematical notation of numbers, see numeral system.
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 (including ordinal numbers like the compound word "seventy-fifth") to a part of speech called "numerals".[1][2] Numerals in the broad sense can also be analyzed as a noun ("three is a small number"), as a pronoun ("the two went to town"), or for a small number of words as an adverb ("I rode the slide twice").
Numerals may be attributive, as in two dogs, or pronominal, as in I saw two (of them).
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.[3] 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. (*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 (adverbial) numbers (once, twice, and thrice), multipliers (single, double, and triple), and distributive numbers (singly, doubly, and triply). Georgian,[4] 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 (monad, pair/dyad, triad) 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[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. 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.
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.
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.[8] In this system, a new word is invented for every 2n-th power of ten.
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 (3/25), 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
Great gross: (based on a group of 1,728 objects or items)
Basis of counting system
Not all peoples use counting, 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 include Nadëb, pre-contact Mocoví and Pilagá, Culina and pre-contact Jarawara, Jabutí, Canela-Krahô, Botocudo (Krenák), Chiquitano, the Campa languages, Arabela, and Achuar.[10] Some languages of Australia, such as Warlpiri, do not have words for quantities above two,[11][12][13] and neither did many Khoisan 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]
No base
Many languages of Melanesia 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.
2: binary
Binary systems are based on the number 2, using zeros and ones. With only two symbols binary is used for things with coding like computers.
Ternary systems are based on the number 3, having practical usage in some analog logic, in baseball scoring and in self–similar mathematical structures.
Quaternary systems are based on the number 4. Some Austronesian, Melanesian, Sulawesi, and Papua New Guinea ethnic groups, count with the base number four, using the term asu or aso, the word for dog, 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 fifty asu heads of pig (200), less 30 asu (120) of pig bartered for 10 asu (40) of goats noting his new pig count total as twenty asu: 80 pigs remaining. The system has a correlation to the dozen 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 the Epi languages of Vanuatu, where 5 is luna 'hand', 10 lua-luna 'two hand', 15 tolu-luna 'three hand', etc. 11 is then lua-luna tai 'two-hand one', and 17 tolu-luna lua 'three-hand two'.
5 is a common auxiliary base, or sub-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 are Kanum and Kómnzo. The Sko languages on the North Coast of New Guinea follow a base-24 system with a sub-base of 6.
7: septenary
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 the Palikúr language has a base-seven system, but this is dubious.[18]
Octal systems are based on the number 8. Examples can be found in the Yuki language of California and in the Pamean languages of Mexico, because the Yuki and Pame keep count by using the four spaces between their fingers rather than the fingers themselves.[19]
9: nonary
Nonary systems are based on the number 9. It has been suggested that Nenets has a base-nine system.[18]
Decimal systems are based on the number 10. A majority of traditional number systems are decimal. This dates back at least to the ancient Egyptians, who used a wholly decimal system. Anthropologists hypothesize this may be due to humans having five digits 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 digit twelve (which is a highly composite number) by many important divisors in market and trade settings, such as the numbers 2, 3, 4 and 6.
Because of several measurements based on twelve,[21] many Western languages have words for base-twelve units such as dozen, gross and great gross, which allow for rudimentary duodecimal nomenclature, such as "two gross six dozen" for 360. Ancient Romans used a decimal system for integers, but switched to duodecimal for fractions, and correspondingly Latin developed a rich vocabulary for duodecimal-based fractions (see Roman numerals). A notable fictional duodecimal system was that of J. R. R. Tolkien's Elvish languages, which used duodecimal as well as decimal.
The traditional Chinese units of measurement were base-16. For example, one jīn(斤) in the old system equals sixteen taels. The suanpan (Chinese abacus) 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 single anna was subdivided into four paisa or twelve pies (thus there were 64 paise or 192 pies in a rupee). The anna was demonetised as a currency unit when India decimalised 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 classical Mesoamerican cultures, still in use today in the modern indigenous languages of their descendants, namely the Nahuatl and Mayan languages (see Maya numerals). A modern national language which uses a full vigesimal system is Dzongkha in Bhutan.
Partial vigesimal systems are found in some European languages: Basque, Celtic languages, French (from Celtic), Danish, and Georgian. 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 term score originates from tally 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 a score of bob", referring to the 20 shillings in a pound. For Americans the term is most known from the opening of the Gettysburg Address: "Four score and seven years ago our fathers...".
24: quadrovigesimal
Quadrovigesimal systems are based on the number 24. The Sko languages have a base-24 system with a sub-base of 6.
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 modern degrees, minutes, and seconds.
80: octogesimal
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 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."
↑ Cardarelli, François (2012). Encyclopaedia of Scientific Units, Weights and Measures: Their SI Equivalences and Origins (Seconded.). Springer. p.585. ISBN978-1447100034.
1 2 Ryan, Peter. Encyclopaedia of Papua and New Guinea. Melbourne University Press & University of Papua and New Guinea,:1972 ISBN0-522-84025-6.: 3 pages p219.
↑ 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.
Chinese numerals are words and characters used to denote numbers in written Chinese.
The decimal numeral system is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as decimal notation.
The duodecimal system, also known as base twelve or dozenal, is a positional numeral system using twelve as its base. In duodecimal, the number twelve is denoted "10", meaning 1 twelve and 0 units; in the decimal system, this number is instead written as "12" meaning 1 ten and 2 units, and the string "10" means ten. In duodecimal, "100" means twelve squared, "1000" means twelve cubed, and "0.1" means a twelfth.
The system of Hebrew numerals is a quasi-decimal alphabetic numeral system using the letters of the Hebrew alphabet. The system was adapted from that of the Greek numerals sometime between 200 and 78 BCE, the latter being the date of the earliest archeological evidence.
A senary numeral system has six as its base. It has been adopted independently by a small number of cultures. Like decimal, it is a semiprime, though it is unique as the product of the only two consecutive numbers that are both prime. As six is a superior highly composite number, many of the arguments made in favor of the duodecimal system also apply to senary.
Thai numerals are a set of numerals traditionally used in Thailand, although the Arabic numerals are more common due to extensive westernization of Thailand in the modern Rattanakosin period. Thai numerals follow the Hindu–Arabic numeral system commonly used in the rest of the world. In Thai language, numerals often follow the modified noun and precede a measure word, although variations to this pattern occur.
English number words include numerals and various words derived from them, as well as a large number of words borrowed from other languages.
A vigesimal or base-20 (base-score) numeral system is based on twenty. Vigesimal is derived from the Latin adjective vicesimus, meaning 'twentieth'.
In written languages, an ordinal indicator is a character, or group of characters, following a numeral denoting that it is an ordinal number, rather than a cardinal number. In English orthography, this corresponds to the suffixes -st, -nd, -rd, -th in written ordinals.
Swedish is descended from Old Norse. Compared to its progenitor, Swedish grammar is much less characterized by inflection. Modern Swedish has two genders and no longer conjugates verbs based on person or number. Its nouns have lost the morphological distinction between nominative and accusative cases that denoted grammatical subject and object in Old Norse in favor of marking by word order. Swedish uses some inflection with nouns, adjectives, and verbs. It is generally a subject–verb–object (SVO) language with V2 word order.
Romanian numbers are the system of number names used in Romanian to express counts, quantities, ranks in ordered sets, fractions, multiplication, and other information related to numbers.
In linguistics, ordinal numerals or ordinal number words are words representing position or rank in a sequential order; the order may be of size, importance, chronology, and so on. They differ from cardinal numerals, which represent quantity and other types of numerals.
The traditional counting system used in the Welsh language is vigesimal, i.e. based on twenties where numbers from 11 to 14 are "x on ten", 16–19 are "x on fifteen" ; numbers from 21 to 39 are "1–19 on twenty", 40 is "two twenty", 60 is "three twenty", etc.
In linguistics, and more precisely in traditional grammar, a cardinal numeral is a part of speech used to count. Examples in English are the words one, two, three, and the compounds three hundred [and] forty-two and nine hundred [and] sixty. Cardinal numerals are classified as definite, and are related to ordinal numbers, such as the English first, second, third, etc.
The Georgian numerals are the system of number names used in Georgian, a language spoken in the country of Georgia. The Georgian numerals from 30 to 99 are constructed using a base-20 system, similar to the scheme used in Basque, French for numbers 80 through 99, or the notion of the score in English.
The names for numerals in Slovene are formed in a similar way to that found in other Slavic languages. An exception is the formation of numerals from 21 to 99, in which the unit is placed in front of the decade ("four-and-twenty"), as in German and Dutch. Many numerals alter their form according to grammatical case, and those from 1 to 4 also according to gender.
The Hokkien language has two regularly used sets of numerals, a colloquial/vernacular or native Hokkien system and literary system that came from Classical Chinese/Middle Chinese that was loaned in for formal written use during medieval times, similar to the Sino-Xenic pronunciations in Japanese, Okinawan, Korean, Jeju, Vietnamese, etc, but within the Sinitic family to the Min group. Literary and colloquial systems are not totally mutually independent; they are sometimes mixed used. The specific pronunciation of each number depends on the specific dialect of Hokkien, which each dialect may either share or use slightly different phonemes and tones on how each dialect may properly count numbers in the Hokkien language for both vernacular and literary systems.
Undecimal is a positional numeral system that uses eleven as its base. While no known society counts by elevens, two are purported to have done so: the Māori and the Pañgwa. The idea of counting by elevens remains of interest for its relation to a traditional method of tally-counting practiced in Polynesia. During the French Revolution, undecimal was briefly considered as a possible basis for the reformed system of measurement. Undecimal numerals have applications in computer science, technology, and the International Standard Book Number system. They also occasionally feature in works of popular fiction. In undecimal, a capital letter or the digit ↊ is typically used as a transdecimal symbol to represent the number 10.
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