In linguistics, a numeral (or number word) in the broadest sense is a
word
A word is a basic element of language that carries an objective or practical meaning, can be used on its own, and is uninterruptible. Despite the fact that language speakers often have an intuitive grasp of what a word is, there is no conse ...
or
phrase
In syntax and grammar, a phrase is a group of words or singular word acting as a grammatical unit. For instance, the English expression "the very happy squirrel" is a noun phrase which contains the adjective phrase "very happy". Phrases can consi ...
that describes a numerical
quantity
Quantity or amount 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 multiple of a u ...
. Some theories of
grammar
In linguistics, the grammar of a natural language is its set of structural constraints on speakers' or writers' composition of clauses, phrases, and words. The term can also refer to the study of such constraints, a field that includes doma ...
use the word "numeral" to refer to
cardinal number
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets. The cardinality of a finite set is a natural number: the number of elements in the set. ...
s that act as a
determiner
A determiner, also called determinative ( abbreviated ), is a word, phrase, or affix that occurs together with a noun or noun phrase and generally serves to express the reference of that noun or noun phrase in the context. That is, a determine ...
that specify the quantity of a
noun
A noun () is a word that generally 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:
* Living creatures (including people, alive, ...
, 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, an adjective ( abbreviated ) is a word that generally modifies a noun or noun phrase or describes its referent. Its semantic role is to change information given by the noun.
Traditionally, adjectives were considered one of the ...
. Some theories consider "numeral" to be a
synonym
A synonym is a word, morpheme, or phrase that means exactly or nearly the same as another word, morpheme, or phrase in a given language. For example, in the English language, the words ''begin'', ''start'', ''commence'', and ''initiate'' are al ...
for "number" and assign all numbers (including
ordinal numbers
In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, th, etc.) aimed to extend enumeration to infinite sets.
A finite set can be enumerated by successively labeling each element with the least ...
like the
compound word
In linguistics, a compound is a lexeme (less precisely, a word or sign) that consists of more than one stem. Compounding, composition or nominal composition is the process of word formation that creates compound lexemes. Compounding occurs when ...
"seventy-fifth") to a
part of speech
In grammar, a part of speech or part-of-speech (abbreviated as POS or PoS, also known as word class or grammatical category) is a category of words (or, more generally, of lexical items) that have similar grammatical properties. Words that are as ...
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 ( 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 parts of speech, but some modern theorists would not ...
("the two went to town"), or for a small number of words as an
adverb An adverb is a word or an expression that generally modifies a verb, adjective, another adverb, determiner, clause, preposition, or sentence. Adverbs typically express manner, place, time, frequency, degree, level of certainty, etc., answering ...
("I rode the slide twice").
Numerals can express relationships like quantity (cardinal numbers),
sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is called ...
(ordinal numbers),
frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
(once, twice), and part (
fraction
A fraction (from la, fractus, "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 ...
).
Identifying numerals
Numerals may be
attributive
In grammar, an attributive expression is a word or phrase within a noun phrase that modifies the head noun. It may be an:
* attributive adjective
* attributive noun
* attributive verb
or other part of speech, such as an attributive numeral.
...
, 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.
[ 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 generally 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:
* Living creatures (including people, alive, ...
, "first" serves the function of an adjective
In linguistics, an adjective ( abbreviated ) is a word that generally modifies a noun or noun phrase or describes its referent. Its semantic role is to change information given by the noun.
Traditionally, adjectives were considered one of the ...
, and "twice" serves the function of an adverb An adverb is a word or an expression that generally modifies a verb, adjective, another adverb, determiner, clause, preposition, or sentence. Adverbs typically express manner, place, time, frequency, degree, level of certainty, etc., answering ...
. 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 and othe ...
, 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 grammar, a part of speech or part-of-speech (abbreviated as POS or PoS, also known as word class or grammatical category) is a category of words (or, more generally, of lexical items) that have similar grammatical properties. Words that are as ...
) 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), a grammatical element used to indicate definiteness or indefiniteness
* Article (publishing), a piece of nonfictional prose that is an independent part of a publication
Article may also refer to:
...
: ''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
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets. The cardinality of a finite set is a natural number: the number of elements in the set. The ...
. 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, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, th, etc.) aimed to extend enumeration to infinite sets.
A finite set can be enumerated by successively labeling each element with the leas ...
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, a distributive numeral, or distributive number word, is a word that answers "how many times each?" or "how many at a time?", such as ''singly'' or ''doubly''. They are contrasted with multipliers. In English, this part of speec ...
s (''singly'', ''doubly'', and ''triply''). Georgian, Latin, and Romanian (see Romanian distributive numbers) have regular distributive number
In linguistics, a distributive numeral, or distributive number word, is a word that answers "how many times each?" or "how many at a time?", such as ''singly'' or ''doubly''. They are contrasted with multipliers. In English, this part of speec ...
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 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
Japanese may refer to:
* Something from or related to Japan, an island country in East Asia
* Japanese language, spoken mainly in Japan
* Japanese people, the ethnic group that identifies with Japan through ancestry or culture
** Japanese diaspor ...
, which uses either native or Chinese-derived numerals depending on what is being counted.
In many languages, such as Chinese, numerals require the use of numeral classifier
A classifier (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. Classifiers play an importan ...
s. Many sign language
Sign languages (also known as signed languages) are languages that use the visual-manual modality to convey meaning, instead of spoken words. Sign languages are expressed through manual articulation in combination with non-manual markers. Sign ...
s, such as ASL, incorporate 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, 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
In grammar, a part of speech or part-of-speech (abbreviated as POS or PoS, also known as word class or grammatical category) is a category of words (or, more generally, of lexical items) that have similar grammatical properties. Words that are as ...
, 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 numeral: C) is the natural number following 99 and preceding 101.
In medieval contexts, it may be described as the short hundred or five score in order to differentiate the English and Germanic use of "hundred" to de ...
102, thousand
1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.
A group of one thousand th ...
103, million
One million (1,000,000), or one thousand thousand, is the natural number following 999,999 and preceding 1,000,001. The word is derived from the early Italian ''millione'' (''milione'' in modern Italian), from ''mille'', "thousand", plus the au ...
106, and higher powers of a thousand (short scale
The long and short scales are two of several naming systems for integer power of 10, 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 m ...
) 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 ...
—see names of large numbers
Two naming scales for large numbers have been used in English and other European languages since the early modern era: the long and short scales. Most English variants use the short scale today, but the long scale remains dominant in many non-Eng ...
). 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 grc, μυριάς, translit=myrias, label=none) is technically the number 10,000 (ten thousand); in that sense, the term is used in English almost exclusively for literal translations from Greek, Latin or Sinospher ...
104, and powers of myriad. In the Indian subcontinent
The Indian subcontinent is a list of the physiographic regions of the world, physiographical region in United Nations geoscheme for Asia#Southern Asia, Southern Asia. It is situated on the Indian Plate, projecting southwards into the Indian O ...
, they are hundred, thousand, lakh
A lakh (; abbreviated L; sometimes written lac) is a unit in the Indian numbering system equal to one hundred thousand (100,000; scientific notation: 105). In the Indian 2,2,3 convention of digit grouping, it is written as 1,00,000. For ex ...
105, crore
A crore (; abbreviated cr) denotes ten million (10,000,000 or 107 in scientific notation) and is equal to 100 lakh in the Indian numbering system. It is written as 1,00,00,000 with the local 2,2,3 style of digit group separators (one lakh is e ...
107, and so on. The Mesoamerican system, 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
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets. The cardinality of a finite set is a natural number: the number of elements in the set. The ...
have numerals. In the following tables, ndindicates that the word ''and'' is used in some dialect
The term dialect (from Latin , , from the Ancient Greek word , 'discourse', from , 'through' and , 'I speak') can refer to either of two distinctly different types of Linguistics, linguistic phenomena:
One usage refers to a variety (linguisti ...
s (such as British English
British English (BrE, en-GB, or BE) is, according to Lexico, Oxford Dictionaries, "English language, English as used in Great Britain, as distinct from that used elsewhere". More narrowly, it can refer specifically to the English language in ...
), and omitted in other dialects (such as American English
American English, sometimes called United States English or U.S. English, is the set of variety (linguistics), varieties of the English language native to the United States. English is the Languages of the United States, most widely spoken lan ...
).
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 numerals and various words derived from them, as well as a large number of words borrowed from other languages.
Cardinal numbers
Cardinal numbers refer to the size of a group. In English, these words are numerals.
...
or names of large numbers
Two naming scales for large numbers have been used in English and other European languages since the early modern era: the long and short scales. Most English variants use the short scale today, but the long scale remains dominant in many non-Eng ...
for more information on naming numbers.
There is no consistent and widely accepted way to extend cardinals beyond centillion
Two naming scales for large numbers have been used in English and other European languages since the early modern era: the long and short scales. Most English variants use the short scale today, but the long scale remains dominant in many non-Eng ...
( centilliard).
Myriad, Octad, and
-yllion
-yllion (pronounced ) is a proposal from Donald Knuth for the terminology and symbols of an alternate decimal superbase system. In it, he adapts the familiar English terms for large numbers to provide a systematic set of names for much larger n ...
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, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (e.g. ). The set of all ration ...
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 infinitely
Infinity is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol .
Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions amo ...
many ways, e.g. ''zero-point-one-two'' (0.12), ''twelve percent
In mathematics, a percentage (from la, per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also use ...
'' (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, a fictional military organization in the science fiction television series ''Doctor Who''
* Unit of action, a discrete piece of action (or beat) in a theatrical presentation
Music
* ''Unit'' (alb ...
: 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 ...
: 2 (the base of the binary numeral system
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" ( one).
The base-2 numeral system is a positional notatio ...
)
* Leash
A leash (also called a lead, lead line or tether) is a rope or similar material used to control an animal by attaching it to a collar, harness, or halter. In British English, a leash is generally for a larger (possibly dangerous or aggressive) ...
: 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, or months, in a cycle of the Sun, or year ...
: 12 (the base of the duodecimal
The duodecimal system (also known as base 12, dozenal, or, rarely, uncial) is a positional notation numeral system using twelve as its base. The number twelve (that is, the number written as "12" in the decimal numerical system) is instead wri ...
numeral system)
* Baker's 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, or months, in a cycle of the Sun, or year ...
: 13
* Score: 20 (the base of the vigesimal
vigesimal () or base-20 (base-score) numeral system is based on twenty (in the same way in which the decimal numeral system is based on ten). '' Vigesimal'' is derived from the Latin adjective '' vicesimus'', meaning 'twentieth'.
Places
In ...
numeral system)
* Shock
Shock may refer to:
Common uses Collective noun
*Shock, a historic commercial term for a group of 60, see English numerals#Special names
* Stook, or shock of grain, stacked sheaves
Healthcare
* Shock (circulatory), circulatory medical emergen ...
: 60 (the base of the sexagesimal
Sexagesimal, also known as base 60 or sexagenary, is a numeral system with sixty as its base. It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians, and is still used—in a modified form ...
numeral system)
* Gross: 144 (= 122)
* Great gross
1728 is the natural number following 1727 and preceding 1729. 1728 is a dozen gross, one great gross (or grand gross).
It is the number of cubic inches in a cubic foot.
It is also the number of daily chants of the Hare Krishna mantra by a Har ...
: 1728 (= 123)
Basis of counting system
Not all peoples count
Count (feminine: countess) is a historical title of nobility in certain European countries, varying in relative status, generally of middling rank in the hierarchy of nobility. Pine, L. G. ''Titles: How the King Became His Majesty''. New York: ...
, 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
The Mocoví ( Mocoví: ''moqoit'') are an indigenous people of the Gran Chaco region of South America. They speak the Mocoví language and are one of the ethnic groups belonging to the Guaycuru peoples. In the 2010 Argentine census, 22,439 peopl ...
and Pilagá, Culina and pre-contact Jarawara, Jabutí, Canela-Krahô, Botocudo (Krenák), Chiquitano
The Chiquitano or Chiquitos are an indigenous people of Bolivia, with a small number also living in Brazil. The Chiquitano primarily live in the Chiquitania tropical savanna of Santa Cruz Department, Bolivia, with a small number also living in Be ...
, the Campa languages
The Campa (Kampa) or Campan (Kampan) languages, a.k.a. Pre-Andine Maipurean / Arawakan, are closely related Arawakan languages of the Peruvian Amazon.
Languages
The Glottolog uses the term ''Pre-Andine'' for this group of languages and classifi ...
, Arabela, and Achuar
The Achuar are an Amazonian community of some 18,500 individuals along either side of the border in between Ecuador and Peru. As of the early 1970s, the Achuar were one of the last of the Jivaroan groups still generally unaffected by outside c ...
. Some languages of Australia, such as Warlpiri, do not have words for quantities above two, and neither did many Khoisan languages
The Khoisan languages (; also Khoesan or Khoesaan) are a group of African languages originally classified together by Joseph Greenberg. Khoisan languages share click consonants and do not belong to other African language families. For much of th ...
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 of Oceania in the southwestern Pacific Ocean. It extends from Indonesia's New Guinea in the west to Fiji in the east, and includes the Arafura Sea.
The region includes the four independent countries of Fiji, Va ...
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, and is that country’s the northernmost island group. The chain of islands that make up this micro-archipelago straddles the broader cultural boundary between Island Melane ...
) 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, using zeros and ones. With only two symbols binary is used for things with coding 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 and Melanesian
Melanesian is the adjectival form of Melanesia. It may refer to:
* Melanesians
* Melanesian mythology
* Melanesian languages In linguistics, Melanesian is an obsolete term referring to the Austronesian languages of Melanesia: that is, the Oceani ...
ethnic groups, some Sulawesi
Sulawesi (), also known as Celebes (), is an island in Indonesia. One of the four Greater Sunda Islands, and the world's eleventh-largest island, it is situated east of Borneo, west of the Maluku Islands, and south of Mindanao and the Sulu Ar ...
and some Papua New Guinea
Papua New Guinea (abbreviated 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 i ...
ns, count with the base number four, using the term ''asu'' and ''aso'', the word for dog
The dog (''Canis familiaris'' or ''Canis lupus familiaris'') is a domesticated descendant of the wolf. Also called the domestic dog, it is derived from the extinct Pleistocene wolf, and the modern wolf is the dog's nearest living relative. Do ...
, 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
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, or months, in a cycle of the Sun, or year ...
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
The half dozen Epi languages are spoken on Epi Island
Epi (or Épi, Api; formerly known as Tasiko or Volcano Island) is an island in Shefa Province, Vanuatu, at the north end of the Shepherd Islands.
The island is long northwest–southeast ...
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
The Aztecs () were a Mesoamerican culture that flourished in central Mexico in the post-classic period from 1300 to 1521. The Aztec people included different Indigenous peoples of Mexico, ethnic groups of central Mexico, particularly those g ...
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 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 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
The Palikur are an indigenous people located in the riverine areas of the Brazilian state of Amapá and in French Guiana, particularly in the south-eastern border region, on the north bank of the Oyapock River. The Palikur Nation, or ''naoné'', ...
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
Yuki, also known as Ukomno'm, is an extinct language of California, formerly spoken by the Yuki people. The Yuki are the original inhabitants of the Eel River area and the Round Valley Reservation of northern California. Yuki ceased to be used ...
of California
California is a U.S. state, state in the Western United States, located along the West Coast of the United States, Pacific Coast. With nearly 39.2million residents across a total area of approximately , it is the List of states and territori ...
and in the Pamean languages of Mexico
Mexico (Spanish: México), officially the United Mexican States, is a country in the southern portion of North America. It is bordered to the north by the United States; to the south and west by the Pacific Ocean; to the southeast by Guatema ...
, because the Yuki and Pame keep count by using the four spaces between their fingers rather than the fingers themselves.
9: nonary
It has been suggested that 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
Egyptians ( arz, المَصرِيُون, translit=al-Maṣriyyūn, ; arz, المَصرِيِين, translit=al-Maṣriyyīn, ; cop, ⲣⲉⲙⲛ̀ⲭⲏⲙⲓ, remenkhēmi) are an ethnic group native to the Nile, Nile Valley in Egypt. Egyptian ...
, who used a wholly decimal system. Anthropologists hypothesize this may be due to humans having five digits per hand, ten in total. There are many regional variations including:
* Western system: based on thousand
1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.
A group of one thousand th ...
s, with variants (see English numerals
English number words include numerals and various words derived from them, as well as a large number of words borrowed from other languages.
Cardinal numbers
Cardinal numbers refer to the size of a group. In English, these words are numerals.
...
)
* Indian system: crore
A crore (; abbreviated cr) denotes ten million (10,000,000 or 107 in scientific notation) and is equal to 100 lakh in the Indian numbering system. It is written as 1,00,00,000 with the local 2,2,3 style of digit group separators (one lakh is e ...
, lakh
A lakh (; abbreviated L; sometimes written lac) is a unit in the Indian numbering system equal to one hundred thousand (100,000; scientific notation: 105). In the Indian 2,2,3 convention of digit grouping, it is written as 1,00,000. For ex ...
(see Indian numbering system
The Indian numbering system is used in all South Asian countries (Bangladesh, Bhutan, India, Maldives, Nepal, Pakistan, Sri Lanka and Afghanistan) to express large numbers. The terms ''lakh'' or 1,00,000 (one hundred thousand, written as ''100,00 ...
. Indian numerals
Indian or Indians may refer to:
Peoples South Asia
* Indian people, people of Indian nationality, or people who have an Indian ancestor
** Non-resident Indian, a citizen of India who has temporarily emigrated to another country
* South Asia ...
)
* East Asian system: based on ten-thousands (see below)
12: duodecimal
Duodecimal systems are based on 12.
These include:
* Chepang language Chepang may refer to:
*Chepang people, a group indigenous to the lands of Nepal
*Chepang language Chepang may refer to:
* Chepang people, a group indigenous to the lands of Nepal
* Chepang language, the language of the Chepang people
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Duodecimal numeric systems have some practical advantages over decimal. It is much easier to divide the base digit
.
Because of several measurements based on twelve, many Western languages have words for base-twelve units such as ''
, such as "two gross six dozen" for 360.
). A notable fictional duodecimal system was that of
, which used duodecimal as well as decimal.
were base-16. For example, one jīn (斤) in the old system equals sixteen