HOME

TheInfoList




In linguistics, a numeral (or number word) in the broadest sense is a
word In linguistics, a word of a spoken language can be defined as the smallest sequence of phonemes that can be uttered in isolation with semantic, objective or pragmatics, practical meaning (linguistics), meaning. In many languages, words also cor ...

word
or
phrase In syntax In linguistics, syntax () is the set of rules, principles, and processes that govern the structure of Sentence (linguistics), sentences (sentence structure) in a given Natural language, language, usually including word order. The ter ...

phrase
that describes a numerical
quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value in terms of a unit of measu ...
. Some theories of
grammar In linguistics Linguistics is the scientific study of language, meaning that it is a comprehensive, systematic, objective, and precise study of language. Linguistics encompasses the analysis of every aspect of language, as well as the me ...
use the word "numeral" to refer to
cardinal number 150px, Aleph null, the smallest infinite cardinal In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and ca ...
s that act as a
determiner A determiner, also called determinative ( abbreviated ), is a word In linguistics, a word of a spoken language can be defined as the smallest sequence of phonemes that can be uttered in isolation with semantic, objective or pragmatics, practic ...
that specify the quantity of a
noun A noun () is a word that functions as the name of a specific object or set of objects, such as living creatures, places, actions, qualities, states of existence, or ideas.Example nouns for: * Organism, Living creatures (including people, alive, de ...

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 In linguistics Linguistics is the scientific study of language A language is a structured system of communication used by humans, including speech (spoken language), gestures (Signed language, sign language) and writing. Most langu ...
. Some theories consider "numeral" to be a
synonym A synonym is a word, morpheme A morpheme is the smallest meaningful lexical item in a language. A morpheme is not a word. The difference between a morpheme and a word is that a morpheme bound and free morphemes, sometimes does not stand alone, ...
for "number" and assign all numbers (including
ordinal numbers In set theory illustrating the intersection (set theory), intersection of two set (mathematics), sets. Set theory is a branch of mathematical logic that studies Set (mathematics), sets, which informally are collections of objects. Although any ...
like the
compound word In linguistics Linguistics is the science, scientific study of language. It encompasses the analysis of every aspect of language, as well as the methods for studying and modeling them. The traditional areas of linguistic analysis include p ...
"seventy-fifth") to a
part of speech In traditional grammar Traditional grammar is a framework for the description of the structure of a language A language is a structured system of communication used by humans, including speech (spoken language), gestures (Signed language, sig ...
called "numerals" Numerals in the broad sense can also be analyzed as a noun ("three is a small number"), as a
pronoun In linguistics and grammar, a pronoun (list of glossing abbreviations, abbreviated ) is a word or a group of words that one may substitute for a noun or noun phrase. Pronouns have traditionally been regarded as one of the part of speech, parts of ...

pronoun
("the two went to town"), or for a small number of words as an
adverb An adverb is a word or an expression that modifies a verb A verb, from the Latin ''wikt:verbum#Latin, verbum'' meaning ''word'', is a word (part of speech) that in syntax conveys an action (''bring'', ''read'', ''walk'', ''run'', ''learn''), ...

adverb
("I rode the slide twice"). Numerals can express relationships like quantity (cardinal numbers),
sequence In , a sequence is an enumerated collection of in which repetitions are allowed and matters. Like a , it contains (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is called the ''length'' of the sequence. Unl ...

sequence
(ordinal numbers),
frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparent ...

frequency
(once, twice), and part (
fraction A fraction (from Latin ', "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths ...
).


Identifying numerals

Numerals may be
attributive In grammar, an attributive expression is a word or phrase within a noun phrase A noun phrase, or nominal (phrase), is a phrase In everyday speech, a phrase is any group of words, often carrying a special idiomatic meaning; in this sense it is syno ...
, as in ''two dogs'', or
pronominal In linguistics and grammar, a pronoun (list of glossing abbreviations, abbreviated ) is a word that substitutes for a noun or noun phrase. Pronouns have traditionally been regarded as one of the part of speech, parts of speech, but some modern th ...
, 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. 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 A noun () is a word that functions as the name of a specific object or set of objects, such as living creatures, places, actions, qualities, states of existence, or ideas.Example nouns for: * Organism, Living creatures (including people, alive, de ...

noun
, "first" serves the function of an
adjective In linguistics Linguistics is the scientific study of language A language is a structured system of communication used by humans, including speech (spoken language), gestures (Signed language, sign language) and writing. Most langu ...
, and "twice" serves the function of an
adverb An adverb is a word or an expression that modifies a verb A verb, from the Latin ''wikt:verbum#Latin, verbum'' meaning ''word'', is a word (part of speech) that in syntax conveys an action (''bring'', ''read'', ''walk'', ''run'', ''learn''), ...

adverb
. In
Old Church Slavonic Old Church Slavonic or Old Slavonic (, ) was the first Slavic literary language. Historians credit the 9th-century Byzantine missionaries Saints Cyril and Methodius with standardizing the language and using it in translating the Bible ...
, 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 In traditional grammar Traditional grammar is a framework for the description of the structure of a language A language is a structured system of communication used by humans, including speech (spoken language), gestures (Signed language, sig ...
) is reserved for those words which have distinct grammatical behavior: when a numeral modifies a noun, it may replace the
article Article often refers to: * Article (grammar) An article is any member of a class of dedicated words that are used with noun phrases to mark the identifiability of the referents of the noun phrases. The category of articles constitutes a part of ...
: ''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 150px, Aleph null, the smallest infinite cardinal In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and ca ...
. 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 number In set theory illustrating the intersection of two sets Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a s ...
s (''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 number In linguistics Linguistics is the science, scientific study of language. It encompasses the analysis of every aspect of language, as well as the methods for studying and modeling them. The traditional areas of linguistic analysis include ...
s (''singly'', ''doubly'', and ''triply'').
Georgian Georgian may refer to: Common meanings * Anything related to, or originating from Georgia (country) **Georgians, an indigenous Caucasian ethnic group **Georgian language, a Kartvelian language spoken by Georgians **Georgian scripts, three scripts ...
, Latin, and Romanian (see Romanian distributive numbers) have regular
distributive number In linguistics Linguistics is the science, scientific study of language. It encompasses the analysis of every aspect of language, as well as the methods for studying and modeling them. The traditional areas of linguistic analysis include ...
s, 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 numeralsIn Russian grammar, the system of declension is elaborate and complex. Nouns, pronouns, adjectives, demonstratives, most numerals and other particles are declined for two grammatical numbers (singular and plural) and six grammatical cases ; some of t ...
,
Polish numeralsThe grammar of the Polish language is characterized by a high degree of inflected language, inflection, and has relatively free word order, although the dominant arrangement is subject–verb–object (SVO). There are no article (grammar), articles, ...
). 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 Japanese may refer to: * Something from or related to Japan , image_flag = Flag of Japan.svg , alt_flag = Centered deep red circle on a white rectangle , image_coat = Imperial Seal of J ...
, which uses either native or Chinese-derived numerals depending on what is being counted. In many languages, such as
Chinese Chinese can refer to: * Something related to China China, officially the People's Republic of China (PRC), is a country in East Asia. It is the List of countries and dependencies by population, world's most populous country, with a populat ...
, numerals require the use of
numeral classifier A classifier (list of glossing abbreviations, abbreviated or ) is a word or affix that accompanies nouns and can be considered to "classify" a noun depending on the type of its referent. It is also sometimes called a measure word or counter word. ...
s. Many
sign language Sign languages (also known as signed languages) are languages that use the visual-manual modality to convey meaning. Sign languages are expressed through manual articulations in combination with non-manual elements. Sign languages are full-fledg ...

sign language
s, such as ,
incorporate Incorporation may refer to: * Incorporation (business), the creation of a corporation * Incorporation of a place, creation of municipal corporation such as a city or county * Incorporation (academic), awarding a degree based on the student having a ...
numerals.


Larger numerals

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 Balinese may refer to: *Bali, an Indonesian island *Balinese art *Balinese dance *Balinese people *Balinese language **Balinese script **Balinese (Unicode block) *Balinese mythology *Balinese cat, a cat breed *Balinese Gamelan, local music *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 Hindustani may refer to: * something of, from, or related to Hindustan (another name of India) * Hindustani language, an Indo-Aryan language, whose two official norms are Hindi and Urdu * Fiji Hindi, a variety of Eastern Hindi spoken in Fiji, and i ...
, 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 In traditional grammar Traditional grammar is a framework for the description of the structure of a language A language is a structured system of communication used by humans, including speech (spoken language), gestures (Signed language, sig ...
, while the words for powers of the base belong to one of the other word classes. In English, these higher words are
hundred 100 or one hundred (Roman numerals, Roman numeral: C) is the natural number following 99 (number), 99 and preceding 101 (number), 101. In medieval contexts, it may be described as the short hundred or five 20 (number), score in order to differenti ...
102,
thousand 1000 or one thousand is the natural number In mathematics, the natural numbers are those used for counting (as in "there are ''six'' coins on the table") and total order, ordering (as in "this is the ''third'' largest city in the country"). ...
103,
million One million (1,000,000), or one thousand thousand, is the natural number In mathematics, the natural numbers are those used for counting (as in "there are ''six'' coins on the table") and total order, ordering (as in "this is the ''third'' l ...

million
106, and higher powers of a thousand ( short scale) or of a million (
long scale The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes. For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two sc ...
—see
names of large numbers This article lists and discusses the usage and derivation of names of large numbers Numbers that are significantly larger than those typically used in everyday life, for instance in simple counting or in monetary transactions, appear frequently i ...
). 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 A myriad (from Ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: M ...
104, and powers of myriad. In India, they are hundred, thousand,
lakh A lakh (; abbreviated L; sometimes written lac) is a unit in the Indian numbering system The Indian numbering system is used in the Indian subcontinent (Bangladesh, Bhutan, India, Maldives, Nepal, Pakistan and Sri Lanka) to express large numbers. ...

lakh
105,
crore A crore (; abbreviated cr), kodi, karod, karor, or koti denotes ten million (10,000,000 or 107 in scientific notation Scientific notation is a way of expressing numbers A number is a mathematical object A mathematical object is an ...
107, and so on. The , still used to some extent in
Mayan languages The Mayan languagesIn linguistics, it is conventional to use ''Mayan'' when referring to the languages, or an aspect of a language. In other academic fields, ''Maya'' is the preferred usage, serving as both a singular and plural noun, and as ...
, was based on powers of 20: ''bak’'' 400 (202), ''pik'' 8000 (203), ''kalab'' 160,000 (204), etc.


Numerals of cardinal numbers

The
cardinal numbers 150px, Aleph null, the smallest infinite cardinal In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and ca ...
have numerals. In the following tables, indicates that the word ''and'' is used in some
dialect The term dialect (from , , from the word , 'discourse', from , 'through' and , 'I speak') can refer to either of two distinctly different types of phenomena: * One usage refers to a of a that is a characteristic of a particular group of ...
s (such as
British English British English (BrE) is the standard dialect A standard language (also standard variety, standard dialect, and standard) is a language variety that has undergone substantial codification of grammar and usage and is employed by a populatio ...
), and omitted in other dialects (such as
American English American English (AmE, AE, AmEng, USEng, en-US), sometimes called United States English or U.S. English, is the set of varieties of the English language native to the United States. Currently, American English is the most influential form of ...
). This table demonstrates the standard English construction of some cardinal numbers. (See next table for names of larger cardinals.)


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 English number words include numeral (linguistics), numerals and various words derived from them, as well as a large number of words borrowed from other languages. Cardinal numbers Cardinal number (linguistics), Cardinal numbers refer to the si ...
or
names of large numbers This article lists and discusses the usage and derivation of names of large numbers Numbers that are significantly larger than those typically used in everyday life, for instance in simple counting or in monetary transactions, appear frequently i ...
for more information on naming numbers. There is no consistent and widely accepted way to extend cardinals beyond
centillion This article lists and discusses the usage and derivation of names of large numbers, together with their possible extensions. The following table lists those names of large numbers that are found in many English dictionaries and thus have a claim ...
( centilliard).


Myriad, Octad, and

-yllion -yllion (pronounced )http://mrob.com/pub/math/largenum-2.html#yllion is a proposal from Donald Knuth Donald Ervin Knuth ( ; born January 10, 1938) is an American computer scientist, mathematician A mathematician is someone who uses an extens ...
systems

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. In this system, a new word is invented for every ''2n''-th power of ten.


Fractional numerals

This is a table of English names for non-negative
rational number In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no ...
s 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 many ways, e.g. ''zero-point-one-two'' (0.12), ''twelve
percent In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no ...

percent
'' (12%), ''three twenty-fifths'' (), ''nine seventy-fifths'' (), ''six fiftieths'' (), ''twelve hundredths'' (), ''twenty-four two-hundredths'' (), etc.


Other specific quantity terms

Various terms have arisen to describe commonly used measured quantities. *
Unit Unit may refer to: Arts and entertainment * UNIT Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) in ...

Unit
: 1 *
Pair Pair or PAIR or Pairing may refer to: Government and politics * Pair (parliamentary convention), matching of members unable to attend, so as not to change the voting margin * ''Pair'', a member of the Prussian House of Lords * ''Pair'', the Frenc ...

Pair
: 2 (the base of the
binary numeral system In mathematics and digital electronics Digital electronics is a field of electronics Electronics comprises the physics, engineering, technology and applications that deal with the emission, flow and control of electrons in vacuum and matter ...
) *
Leash A leash (also called a lead, lead line or tether A tether is a cord, fixture, or flexible attachment that anchors something movable to a reference point which may be fixed or moving. There are a number of applications for tethers: balloons, ki ...

Leash
: 3 (the base of the trinary numeral system) *
Dozen A dozen (commonly abbreviated doz or dz) is a grouping of twelve. The dozen may be one of the earliest primitive integer groupings, perhaps because there are approximately a dozen cycles of the Moon The Moon is Earth's only natural sat ...
: 12 (the base of the
duodecimal The duodecimal system (also known as base 12, dozenal, or, rarely, uncial) is a positional notation Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any radix, base of the Hindu–Arabi ...
numeral system) *
Baker's dozen A dozen (commonly abbreviated doz or dz) is a grouping of 12 (number), twelve. The dozen may be one of the earliest primitive groupings, perhaps because there are approximately a dozen cycles of the Moon, or months, in a cycle of the Sun, or yea ...
: 13 *
Score Score or scorer may refer to: *Test score, the result of an exam or test Business * Score Digital, now part of Bauer Radio#Score Digital, Bauer Radio * Score Entertainment, a former American trading card design and manufacturing company * Score ...
: 20 (the base of the
vigesimal A vigesimal () or base-20 (base-score) numeral system is based on 20 (number), twenty (in the same way in which the decimal, decimal numeral system is based on 10 (number), ten). ''wikt:vigesimal#English, Vigesimal'' is derived from the Latin adje ...
numeral system) * Shock: 60 (the base of the
sexagesimal Sexagesimal, also known as base 60 or sexagenary, is a numeral system A numeral system (or system of numeration) is a writing system A writing system is a method of visually representing verbal communication Communication (from Latin ...
numeral system) * Gross: 144 (= 122) *
Great gross 1728 is the natural number In mathematics, the natural numbers are those used for counting (as in "there are ''six'' coins on the table") and total order, ordering (as in "this is the ''third'' largest city in the country"). In common mathemat ...
: 1728 (= 123)


Basis of counting system

Not all peoples
count Count (feminine: countess) is a historical title of nobility Nobility is a social class normally ranked immediately below Royal family, royalty and found in some societies that have a formal aristocracy (class), aristocracy. Nobility ...
, 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're 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 Chiquitano or Chiquitos are an indigenous people Indigenous peoples, also referred to as First people, Aboriginal people, Native people, or autochthonous people, are culturally distinct ethnic groups who are native to a particular place. ...
, the
Campa languages The Campa (Kampa) or Campan (Kampan) languages, a.k.a. Pre-Andine Maipurean / Arawakan, are closely related Arawakan languages Arawakan (''Arahuacan, Maipuran Arawakan, "mainstream" Arawakan, Arawakan proper''), also known as Maipurean (also ''M ...
, , and
Achuar The Achuar are an Amazonian community of some 18,500 individuals along either side of the border in between Ecuador Ecuador ( ; ; Quechua Quechua may refer to: *Quechua people, several indigenous ethnic groups in South America, especial ...
. Some languages of Australia, such as Warlpiri, do not have words for quantities above two, as did many
Khoisan languages The Khoisan languages (; also Khoesan or Khoesaan) are a group of Languages of Africa, African languages originally classified together by Joseph Greenberg. Khoisan languages share click languages, click consonants and do not belong to other Afri ...

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).


No base

Many languages of
Melanesia Melanesia (, ) is a subregion A subregion is a part of a larger region In geography Geography (from Greek: , ''geographia'', literally "earth description") is a field of science devoted to the study of the lands, features, inhabi ...

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 The Torres Islands are in the Torba Province of the country of Vanuatu Vanuatu ( or ; ), officially the Republic of Vanuatu (french: link=no, République de Vanuatu; Bislama: ''Ripablik blong Vanuatu''), is an island country located in th ...
) 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 base 2, often using zeros and ones. With only two symbols binary is useful for logical systems like computers.


3: ternary

Base 3 counting has practical usage in some analog logic, in baseball scoring and in self–similar mathematical structures.


4: quaternary

Some
Austronesian Austronesian may refer to: *The Austronesian languages *The historical Austronesian peoples who carried Austronesian languages on their migrations {{disambiguation ...
and
Melanesian Melanesians are the predominant and indigenous inhabitants of Melanesia, in a wide area from Maluku Islands and New Guinea New Guinea (; Hiri Motu: ''Niu Gini''; id, Papua, historically ) is the List of islands by area, world's second-l ...

Melanesian
ethnic groups, some
Sulawesi Sulawesi (), also known as Celebes (), is one of the four Greater Sunda Islands The Greater Sunda Islands are four tropical islands situated within Southeast Asia, in the Pacific Ocean. The islands, Borneo, Java, Sulawesi and Sumatra, are i ...

Sulawesi
and some
Papua New Guinea Papua New Guinea (PNG; , ; tpi, Papua Niugini; ho, Papua Niu Gini), officially the Independent State of Papua New Guinea ( tpi, Independen Stet bilong Papua Niugini; ho, Independen Stet bilong Papua Niu Gini), is a country in Oceania th ...

Papua New Guinea
ns, count with the base number four, using the term ''asu'' and ''aso'', the word for
dog The dog or domestic dog (''Canis familiaris'' or ''Canis lupus familiaris'') is a domesticated Domestication is a sustained multi-generational relationship in which one group of organisms assumes a significant degree of influence over the ...

dog
, as the ubiquitous village dog has four legs.Ryan, Peter. ''Encyclopaedia of Papua and New Guinea''. Melbourne University Press & University of Papua and New Guinea,:1972 .: 3 pages p 219. 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.


5: quinary

Quinary systems are based on the number 5. It is almost certain the quinary system developed from counting by fingers (five fingers per hand).Heath, Thomas, ''A Manual of Greek Mathematics'', Courier Dover: 2003. page, p:11 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. Nahua language, Aztec was a vigesimal (base-20) system with sub-base 5.


6: senary

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 language, Kanum and Kómnzo language, 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 very rare, as few natural objects consistently have seven distinctive features. Traditionally, it occurs in week-related timing. It has been suggested that the Palikur language has a base-seven system, but this is dubious.Parkvall, M. ''Limits of Language'', 1st edn. 2008. p.291.


8: octal

Octal counting 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 tribe, Yuki and Pame people, Pame keep count by using the four spaces between their fingers rather than the fingers themselves.


9: nonary

It has been suggested that Nenets languages, Nenets has a base-nine system.


10: decimal

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 digit (anatomy), digits per hand, ten in total. There are many regional variations including: * Western system: based on one thousand, thousands, with variants (see
English numerals English number words include numeral (linguistics), numerals and various words derived from them, as well as a large number of words borrowed from other languages. Cardinal numbers Cardinal number (linguistics), Cardinal numbers refer to the si ...
) * Indian system:
crore A crore (; abbreviated cr), kodi, karod, karor, or koti denotes ten million (10,000,000 or 107 in scientific notation Scientific notation is a way of expressing numbers A number is a mathematical object A mathematical object is an ...
,
lakh A lakh (; abbreviated L; sometimes written lac) is a unit in the Indian numbering system The Indian numbering system is used in the Indian subcontinent (Bangladesh, Bhutan, India, Maldives, Nepal, Pakistan and Sri Lanka) to express large numbers. ...

lakh
(see Indian numbering system. Indian numerals) * East Asian system: based on 10000 (number), ten-thousands (see below)


12: duodecimal

Duodecimal systems are based on 12. These include: * Chepang language of Nepal, * Mahl language of Minicoy Island in India * Nigerian Middle Belt areas such as Janji language, Janji, Kahugu language, Kahugu and the Nimbia dialect of Gwandara language, Gwandara. *
Melanesia Melanesia (, ) is a subregion A subregion is a part of a larger region In geography Geography (from Greek: , ''geographia'', literally "earth description") is a field of science devoted to the study of the lands, features, inhabi ...

Melanesia
* reconstructed proto-Benue–Congo Duodecimal numeric systems have some practical advantages over decimal. It is much easier to divide the base digit 12 (number), twelve (which is a highly composite number) by many important divisors in Market (economics), market and trade settings, such as the numbers 2 (number), 2, 3 (number), 3, 4 (number), 4 and 6 (number), 6. Because of several measurements based on twelve, many Western languages have words for base-twelve units such as ''dozen'', ''Gross (unit), gross'' and ''great gross'', which allow for rudimentary duodecimal nomenclature, such as "two gross six dozen" for 360. Ancient Rome, Ancient Romans used a decimal system for integers, but switched to
duodecimal The duodecimal system (also known as base 12, dozenal, or, rarely, uncial) is a positional notation Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any radix, base of the Hindu–Arabi ...
for fractions, and correspondingly Latin developed a rich vocabulary for duodecimal-based fractions (see Roman numerals#Fractions, Roman numerals). A notable fictional duodecimal system was that of J. R. R. Tolkien's Elvish languages, which used duodecimal as well as decimal.


16: hexadecimal

Hexadecimal systems are based on 16. 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. South Asian monetary systems were base-16. One rupee in Pakistan and India was divided into 16 annay. A single Indian anna, anna was subdivided into four paisa or twelve Pie (Indian coin), pies (thus there were 64 paise or 192 pies in a rupee). The anna was Legal tender#Demonetization, demonetised as a currency unit when India Decimalisation, decimalised its currency in 1957, followed by Pakistan in 1961.


20: vigesimal

Vigesimal numbers use the number 20 as the base number for counting. 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.Georges Ifrah, ''The Universal History of Numbers: The Modern Number System'', Random House, 2000: . 1262 pages 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 The Mayan languagesIn linguistics, it is conventional to use ''Mayan'' when referring to the languages, or an aspect of a language. In other academic fields, ''Maya'' is the preferred usage, serving as both a singular and plural noun, and as ...
(see Maya numerals). A modern national language which uses a full vigesimal system is Dzongkha language, Dzongkha in Bhutan. Partial vigesimal systems are found in some European languages: Basque language, Basque, Celtic languages, French language, French (from Celtic), Danish language, Danish, and
Georgian Georgian may refer to: Common meanings * Anything related to, or originating from Georgia (country) **Georgians, an indigenous Caucasian ethnic group **Georgian language, a Kartvelian language spoken by Georgians **Georgian scripts, three scripts ...
. 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 ''20 (number), 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 20 (number), score of shilling, bob", referring to the 20 British shilling coin, shillings in a pound sterling#Pre-decimal, 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

The Sko languages have a base-24 system with a sub-base of 6.


32: duotrigesimal

Ngiti language, Ngiti has base 32.


60: sexagesimal

Ekari language, 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 degree (angle), degrees, minutes, and seconds.


80: octogesimal

Supyire language, 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). 799 [i.e. 400 + (4 x 80) + (3 x 20) + ]’


See also


Numerals in various languages

A databas
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 **
English numerals English number words include numeral (linguistics), numerals and various words derived from them, as well as a large number of words borrowed from other languages. Cardinal numbers Cardinal number (linguistics), Cardinal numbers refer to the si ...
** Indian numbering system **
Polish numeralsThe grammar of the Polish language is characterized by a high degree of inflected language, inflection, and has relatively free word order, although the dominant arrangement is subject–verb–object (SVO). There are no article (grammar), articles, ...
** Hindustani numerals * Proto-Semitic numerals ** Hebrew numerals * Chinese numerals ** Japanese numerals ** Korean numerals **Vietnamese numerals * Australian Aboriginal enumeration * Balinese numerals * Dzongkha numerals * Finnish numerals * Javanese numerals * Yoruba numerals


Related topics

* Long and short scales * Names of large numbers * Numeral system * Numeral prefix * Names of small numbers


Notes


Further reading

* {{DEFAULTSORT:Number Names Numerals, * Names