In linguistics, a numeral in the broadest sense is a

word A word is a basic element of language that carries semantics, 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 consensus among linguist ...

phrase In grammar, a phrasecalled expression in some contextsis a group of words or singular word acting as a grammatical unit. For instance, the English language, English expression "the very happy squirrel" is a noun phrase which contains the adject ...

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, grammar is the set of rules for how a natural language is structured, as demonstrated by its speakers or writers. Grammar rules may concern the use of clauses, phrases, and words. The term may also refer to the study of such rul ...

use the word "numeral" to refer to

cardinal number In mathematics, a cardinal number, or cardinal for short, is what is commonly called the number of elements of a set. In the case of a finite set, its cardinal number, or cardinality is therefore a natural number. For dealing with the cas ...

s that act as a

determiner Determiner, also called determinative ( abbreviated ), is a term used in some models of grammatical description to describe a word or affix belonging to a class of noun modifiers. A determiner combines with a noun to express its reference. Examp ...

that specify the quantity of a

noun In grammar, a noun is a word that represents a concrete or abstract thing, like living creatures, places, actions, qualities, states of existence, and ideas. A noun may serve as an Object (grammar), object or Subject (grammar), subject within a p ...

, 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 An adjective (abbreviations, abbreviated ) is a word that describes or defines a noun or noun phrase. Its semantic role is to change information given by the noun. Traditionally, adjectives are considered one of the main part of speech, parts of ...

. Some theories consider "numeral" to be a

synonym A synonym is a word, morpheme, or phrase that means precisely 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 a ...

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 leas ...

like "first") 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 ...

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 (Interlinear gloss, glossed ) 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 speech, but so ...

("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, an adjective, another adverb, a determiner, a clause, a preposition, or a sentence. Adverbs typically express manner, place, time, frequency, degree, or level of certainty by ...

("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 cal ...

(ordinal numbers),

frequency Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...

(once, twice), and part (

fraction A fraction (from , "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, thre ...

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 In linguistics and grammar, a pronoun ( glossed ) 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 con ...

, 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

, "first" serves the function of an

, and "twice" serves the function of an

. In

Old Church Slavonic Old Church Slavonic or Old Slavonic ( ) is the first Slavic languages, Slavic literary language and the oldest extant written Slavonic language attested in literary sources. It belongs to the South Slavic languages, South Slavic subgroup of the ...

, 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

) 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 In mathematics, a cardinal number, or cardinal for short, is what is commonly called the number of elements of a set. In the case of a finite set, its cardinal number, or cardinality is therefore a natural number. For dealing with the case ...

. 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

s, such as Latin "one-by-one", "in pairs, two-by-two", "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 In 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 ...

Polish numerals The grammar of the Polish language is complex and characterized by a high degree of inflection, and has relatively free word order, although the dominant arrangement is subject–verb–object (SVO). There commonly are no articles (although this ...

). Some languages have a very limited set of numerals, and in some cases they arguably do not have any numerals at all, but instead use more generic quantifiers, such as 'pair' or 'many'. However, by now most such languages have borrowed the numeral system or part of the numeral system of a national or colonial language, though in a few cases (such as Guarani), a numeral system has been invented internally rather than borrowed. Other languages had an indigenous system but borrowed a second set of numerals anyway. An example is Japanese, which uses either native or Chinese-derived numerals depending on what is being counted. In many languages, such as Chinese, numerals require the use of numeral classifiers. 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 elements, no ...

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

, 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 mathematics 100 is the square of 10 (number), 10 (in scientific notation it is written as 102). The standar ...

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 ...

10³,

million 1,000,000 (one million), 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 ...

10⁶, and higher powers of a thousand ( short scale) or of a million (

long scale The long and short scales are two powers of ten number naming systems that are consistent with each other for smaller numbers, but are contradictory for larger numbers. Other numbering systems, particularly in East Asia and South Asia, ha ...

—see

names of large numbers Depending on context (e.g. language, culture, region), some large numbers have names that allow for describing large quantities in a textual form; not mathematical. For very large values, the text is generally shorter than a decimal numeric repre ...

). 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 In the context of numeric naming systems for powers of ten, myriad is the quantity ten thousand ( 10,000). Idiomatically, in English, ''myriad'' is an adjective used to mean that a group of things has indefinitely large quantity. ''Myriad ...

10⁴, and powers of myriad. In the

Indian subcontinent The Indian subcontinent is a physiographic region of Asia below the Himalayas which projects into the Indian Ocean between the Bay of Bengal to the east and the Arabian Sea to the west. It is now divided between Bangladesh, India, and Pakista ...

, 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. F ...

10⁵,

crore Crore (; abbreviated cr) denotes the quantity ten million (107) and is equal to 100 lakh in the Indian numbering system. In many international contexts, the decimal quantity is formatted as 10,000,000, but when used in the context of the India ...

10⁷, and so on. The Mesoamerican system, still used to some extent in

Mayan languages The Mayan languages In 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 a ...

, was based on powers of 20: ''bak’'' 400 (20²), ''pik'' 8000 (20³), ''kalab'' 160,000 (20⁴), etc.

Numerals of cardinal numbers

The

have numerals. In the following tables, ndindicates that the word ''and'' is used in some

dialect A dialect is a Variety (linguistics), variety of language spoken by a particular group of people. This may include dominant and standard language, standardized varieties as well as Vernacular language, vernacular, unwritten, or non-standardize ...

s (such as

British English British English is the set of Variety (linguistics), varieties of the English language native to the United Kingdom, especially Great Britain. More narrowly, it can refer specifically to the English language in England, or, more broadly, to ...

), 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 lang ...

). 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. ...

for more information on naming numbers. There is no consistent and widely accepted way to extend cardinals beyond centillion ( centilliard).

Myriad, Octad, and -yllion systems

The following table details the myriad, octad, Ancient Greek Archimedes's notation, Chinese myriad, Chinese long and -yllion names for powers of 10. There is also 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 (for example, The set of all ...

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 many ways, e.g. ''zero-point-one-two'' (0.12), ''twelve

percent In mathematics, a percentage () 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 used. A percentage is a dime ...

'' (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: General measurement * Unit of measurement, a definite magnitude of a physical quantity, defined and adopted by convention or by law **International System of Units (SI), modern form of the metric system **English units, histo ...

: 1 (based on a single entity of counting or measurement of an object or item) *

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 Fren ...

: 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 for representing numbers that uses only two symbols for the natural numbers: typically "0" ( zero) and "1" ( one). A ''binary number'' may als ...

) * 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, or months, in a cycle of the Sun, or year ...

: 12 (the base of the

duodecimal 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 i ...

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 (based on a group of thirteen objects or items) *

Score SCORE may refer to: *SCORE (software), a music scorewriter program * SCORE (television), a weekend sports service of the defunct Financial News Network *SCORE! Educational Centers *SCORE International, an offroad racing organization *Sarawak Corrido ...

: 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 a ...

numeral system) *

Shock Shock may refer to: Common uses Healthcare * Acute stress reaction, also known as psychological or mental shock ** Shell shock, soldiers' reaction to battle trauma * Circulatory shock, a medical emergency ** Cardiogenic shock, resulting from ...

: 60 (the base of the

sexagesimal Sexagesimal, also known as base 60, is a numeral system with 60 (number), sixty as its radix, 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 fo ...

numeral system) * Gross: (based on a group of 144 objects or items) * Great gross: (based on a group of 1,728 objects or items)

Basis of counting system

Not all peoples use

counting Counting is the process of determining the number of elements of a finite set of objects; that is, determining the size of a set. The traditional way of counting consists of continually increasing a (mental or spoken) counter by a unit for ever ...

, 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 fThe Pilagá (in Pilagá language, Pilagá language: ''pit'laxá'') are an Indigenous peoples of the Americas, indigenous people of the Guaycuru peoples, Guaycuru group that inhabits the center of the province of Formosa Province, Formosa, in Arge ...

, Culina and pre-contact Jarawara, Jabutí, Canela-Krahô, Botocudo (Krenák), Chiquitano, the Campa languages, Arabela, and Achuar. 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 number of Languages of Africa, African languages once classified together, originally by Joseph Greenberg. Khoisan is defined as those languages that have click languages, click consonant ...

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 New Guinea in the west to the Fiji Islands in the east, and includes the Arafura Sea. The region includes the four independent countries of Fiji, Vanu ...

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 an island chain in the Torba Province of the country of Vanuatu, the country’s northernmost island group. The chain of islands that make up this micro-archipelago straddles the broader cultural boundary between Island Me ...

) 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. Due to its simplicity, only having two distinct digits, binary is commonly used in computing, with zero and one often corresponding to "off/on" respectively.

3: ternary

Ternary systems are based on the number 3, having practical usage in some analog logic, in baseball scoring and in self–similar mathematical structures.

4: quaternary

Quaternary systems are based on the number 4. Some Austronesian, Melanesian,

Sulawesi Sulawesi ( ), also known as Celebes ( ), is an island in Indonesia. One of the four Greater Sunda Islands, and the List of islands by area, world's 11th-largest island, it is situated east of Borneo, west of the Maluku Islands, and south of Min ...

, and

Papua New Guinea Papua New Guinea, officially the Independent State of Papua New Guinea, is an island country in Oceania that comprises the eastern half of the island of New Guinea and offshore islands in Melanesia, a region of the southwestern Pacific Ocean n ...

ethnic groups, count with the base number four, using the term ''asu'' or ''aso'', the word for

dog The dog (''Canis familiaris'' or ''Canis lupus familiaris'') is a domesticated descendant of the gray wolf. Also called the domestic dog, it was selectively bred from a population of wolves during the Late Pleistocene by hunter-gatherers. ...

, 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 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 civilization that flourished in central Mexico in the Post-Classic stage, post-classic period from 1300 to 1521. The Aztec people included different Indigenous peoples of Mexico, ethnic groups of central ...

was a vigesimal (base-20) system with sub-base 5.

6: senary

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 Palikúr (Brazilian Portuguese: ''Palicur'', French (language), French: ''Palikur'') is an Arawakan language of Brazil and French Guiana. Knowledge of French language, French and Portuguese language, Portuguese is common among the Palikur, and ...

has a base-seven system, but this is dubious.Parkvall, M. ''Limits of Language'', 1st edn. 2008. p.291.

8: octal

Octal 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 use ...

California California () is a U.S. state, state in the Western United States that lies on the West Coast of the United States, Pacific Coast. It borders Oregon to the north, Nevada and Arizona to the east, and shares Mexico–United States border, an ...

and in the Pamean languages of

Mexico Mexico, officially the United Mexican States, is a country in North America. It is the northernmost country in Latin America, and borders the United States to the north, and Guatemala and Belize to the southeast; while having maritime boundar ...

, because the Yuki and Pame keep count by using the four spaces between their fingers rather than the fingers themselves.

9: nonary

Nonary systems are based on the number 9. It has been suggested that Nenets has a base-nine system.

10: decimal

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 Egyptians (, ; , ; ) are an ethnic group native to the Nile, Nile Valley in Egypt. Egyptian identity is closely tied to Geography of Egypt, geography. The population is concentrated in the Nile Valley, a small strip of cultivable land stretchi ...

, 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

s, with variants (see

) * Indian system:

(see

Indian numbering system The Indian numbering system is used in India, Pakistan, Nepal, Sri Lanka, and Bangladesh to express large numbers, which differs from the International System of Units. Commonly used quantities include ''lakh'' (one hundred thousand) and ''crore' ...

Indian numerals Indian or Indians may refer to: Associated with India * of or related to India ** Indian people ** Indian diaspora ** Languages of India ** Indian English, a dialect of the English language ** Indian cuisine Associated with indigenous peopl ...

) * East Asian system: based on ten-thousands (see below)

12: duodecimal

Duodecimal systems are based on the number 12. These include: *

Chepang language Chepang is a language spoken by approximately 59,000 people in South-Central Nepal. The people are known as Chepang. In 2003, Randy LaPolla proposed that the Chepang may be part of a larger " Rung" group. Another group who speaks Chepang, livin ...

Nepal Nepal, officially the Federal Democratic Republic of Nepal, is a landlocked country in South Asia. It is mainly situated in the Himalayas, but also includes parts of the Indo-Gangetic Plain. It borders the Tibet Autonomous Region of China Ch ...

, * Mahl language of

Minicoy Island Minicoy, locally known as Maliku (), is an island in Lakshadweep, India. Along with Viringili, it is on Maliku atoll, the southernmost atoll of Lakshadweep archipelago. Administratively, it is a census town in the Indian union territory of Laks ...

India India, officially the Republic of India, is a country in South Asia. It is the List of countries and dependencies by area, seventh-largest country by area; the List of countries by population (United Nations), most populous country since ...

Nigerian Nigerians or the Nigerian people are citizens of Nigeria or people with ancestry from Nigeria. The name Nigeria was derived from the Niger River running through the country. This name was allegedly coined in the late 19th century by British jo ...

Middle Belt Middle Belt (also spelt Middle-Belt) or Central Nigeria is a term used in human geography to designate a belt region stretching across central Nigeria longitudinally and forming a transition zone between Northern and Southern Nigeria. It is ...

areas such as Janji, Kahugu and the Nimbia dialect of Gwandara. *

* reconstructed proto- Benue–Congo 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 A highly composite number is a positive integer that has more divisors than all smaller positive integers. If ''d''(''n'') denotes the number of divisors of a positive integer ''n'', then a positive integer ''N'' is highly composite if ''d''(' ...

) by many important divisors in

market Market is a term used to describe concepts such as: *Market (economics), system in which parties engage in transactions according to supply and demand *Market economy *Marketplace, a physical marketplace or public market *Marketing, the act of sat ...

and trade settings, such as the numbers 2, 3, 4 and 6. Because of several measurements based on twelve, many Western languages have words for base-twelve units such as ''

'', '' gross'' and '' great gross'', which allow for rudimentary duodecimal

nomenclature Nomenclature (, ) is a system of names or terms, or the rules for forming these terms in a particular field of arts or sciences. (The theoretical field studying nomenclature is sometimes referred to as ''onymology'' or ''taxonymy'' ). The principl ...

, such as "two gross six dozen" for 360.

Ancient Romans The Roman people was the ethnicity and the body of Roman citizenship, Roman citizens (; ) during the Roman Kingdom, the Roman Republic, and the Roman Empire. This concept underwent considerable changes throughout the long history of the Roman ...

used a decimal system for

integers An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...

, but switched to

for

fractions A fraction (from , "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, thre ...

, and correspondingly

Latin Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area aroun ...

developed a rich vocabulary for duodecimal-based fractions (see

Roman numerals Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, eac ...

). A notable fictional duodecimal system was that of

J. R. R. Tolkien John Ronald Reuel Tolkien (, 3 January 1892 – 2 September 1973) was an English writer and philologist. He was the author of the high fantasy works ''The Hobbit'' and ''The Lord of the Rings''. From 1925 to 1945, Tolkien was the Rawlinson ...

's Elvish languages, which used duodecimal as well as decimal.

16: hexadecimal

Hexadecimal systems are based on the number 16. The traditional

Chinese units of measurement Chinese units of measurement, known in Chinese as the ''shìzhì'' ("market system"), are the traditional units of measurement of the Han Chinese. Although Chinese numerals have been decimal (base-10) since the Shang dynasty, Shang, several Chine ...

were base-16. For example, one jīn (斤) in the old system equals sixteen

tael Tael ( ),"Tael" entry
at the

suanpan (Chinese

abacus An abacus ( abaci or abacuses), also called a counting frame, is a hand-operated calculating tool which was used from ancient times in the ancient Near East, Europe, China, and Russia, until the adoption of the Hindu–Arabic numeral system. A ...

) 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 anna was subdivided into four

paisa Paisa (also transliterated as ''pice'', ''pesa'', ''poysha'', ''poisha'' and ''baisa'') is a monetary unit in several countries. The word is also a generalised idiom for money and wealth. In India, Nepal, and Pakistan, the ''paisa'' currently equa ...

or twelve

pies A pie is a Baking, baked dish which is usually made of a pastry dough casing that contains a filling of various sweetness, sweet or Savoury taste, savoury ingredients. Sweet pies may be filled with fruit (as in an apple pie), nuts (pecan pie) ...

(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.

20: vigesimal

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.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

Mesoamerica Mesoamerica is a historical region and cultural area that begins in the southern part of North America and extends to the Pacific coast of Central America, thus comprising the lands of central and southern Mexico, all of Belize, Guatemala, El S ...

n cultures, still in use today in the modern indigenous languages of their descendants, namely the

Nahuatl Nahuatl ( ; ), Aztec, or Mexicano is a language or, by some definitions, a group of languages of the Uto-Aztecan language family. Varieties of Nahuatl are spoken by about Nahuas, most of whom live mainly in Central Mexico and have smaller popul ...

and

(see

Maya numerals The Mayan numeral system was the system to represent numbers and calendar dates in the Maya civilization. It was a vigesimal (base-20) positional notation, positional numeral system. The numerals are made up of three symbols: Zero number#The ...

). A modern national language which uses a full vigesimal system is

Dzongkha Dzongkha (; ) is a Tibeto-Burman languages, Tibeto-Burman language that is the official and national language of Bhutan. It is written using the Tibetan script. The word means "the language of the fortress", from ' "fortress" and ' "language ...

in Bhutan. Partial vigesimal systems are found in some languages:

Basque Basque may refer to: * Basques, an ethnic group of Spain and France * Basque language, their language Places * Basque Country (greater region), the homeland of the Basque people with parts in both Spain and France * Basque Country (autonomous co ...

Celtic languages The Celtic languages ( ) are a branch of the Indo-European language family, descended from the hypothetical Proto-Celtic language. The term "Celtic" was first used to describe this language group by Edward Lhuyd in 1707, following Paul-Yve ...

, 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 SCORE may refer to: *SCORE (software), a music scorewriter program * SCORE (television), a weekend sports service of the defunct Financial News Network *SCORE! Educational Centers *SCORE International, an offroad racing organization *Sarawak Corrido ...

'' originates from

tally stick A tally stick (or simply a tally) was an ancient memory aid used to record and document numbers, quantities, and messages. Tally sticks first appear as animal bones carved with notches during the Upper Palaeolithic; a notable example is the Is ...

s, 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

of bob", referring to the 20

shilling The shilling is a historical coin, and the name of a unit of modern currency, currencies formerly used in the United Kingdom, Australia, New Zealand, other British Commonwealth countries and Ireland, where they were generally equivalent to 1 ...

s in a pound. For Americans the term is most known from the opening of the

Gettysburg Address The Gettysburg Address is a Public speaking, speech delivered by Abraham Lincoln, the 16th President of the United States, U.S. president, following the Battle of Gettysburg during the American Civil War. The speech has come to be viewed as one ...

: ''"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.

32: duotrigesimal

Duotrigesimal systems are based on the number 32. The Ngiti ethnolinguistic group uses a base 32 numeral system.

60: sexagesimal

Sexagesimal systems are based on the number 60. Ekari has a base-60 system.

Sumer Sumer () is the earliest known civilization, located in the historical region of southern Mesopotamia (now south-central Iraq), emerging during the Chalcolithic and Early Bronze Age, early Bronze Ages between the sixth and fifth millennium BC. ...

ia 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). 799 .e. 400 + (4 x 80) + (3 x 20) + ��