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In linguistics, number names (or numerals) are specific words in a natural language that represent numbers.

In writing, numerals are symbols also representing numbers.

Numeral types

In linguistics, the terms representing numbers can be classified according to their use:
  • Cardinal numerals: describe quantity - one, two, three, etc.
  • Ordinal numerals: describe position in a sequential order - first, second, third, etc.; the terms next and last may also be considered a kind of ordinals.
  • Partitive numerals: describe division into fractions - half, third, quarter, etc.
  • Multiplicative numerals: describe repetition - once, twice, thrice, etc.
  • Collective numerals: describe groups or entities composed of several parts - single, double, triple, etc.
  • Distributive numerals: describe dividing and assigning in portions - in pairs, by the dozen. Note that the English language does not have distinct distributive numerals (though it does have distributive adjectives/pronouns, such as each, either and every), but some other languages such as Georgian and Latin do have them; e.g., Latin singuli ("one by one"), bini ("in pairs", "by twos"), terni ("three each"), etc. (whence the English terms singular, binary, ternary, etc.).

Basis of counting system

Not all peoples count. 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,—or at least didn't 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 numerals other than 'one'; it's arguable that such a system should not be considered a separate word class of 'numeral' at all. These include Nadëb, pre-contact Mocoví and Pilagá, Culina and pre-contact Jarawara, Jabutí, Canela-Krahô, Botocudo , Chiquitano, the Campa languages, Arabela, and Achuar.

4: quaternary

Some Austronesian and Melanesian ethnic groups, including the Maori, some Sulawesimarker and some Papua New Guineansmarker count instead of by five, using the base number four, using the term asu and aso (derived from Javanese asu: dog)- as the ubiquitous village dog has four legs. 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 form 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 twentyasu: 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. Anthropologists argue it is almost certain quinary system developed from counting by fingers (five fingers per hand). It is common since the days of the ancient Babylonians and found in almost every culture worldwide. It is present in the Celtic and Banish systems and the Inuit languages.The ancient Greek Bëotius records that the term digit is exactly that as used to describe fingers- still present today.

8: octal

Octal is a counting system based around the number 8. It is used in the Yuki language of Californiamarker and in the Pamean languages of Mexicomarker, because the Yuki and Pamean keep count by using the four spaces between their fingers rather than the fingers (five) themselves.

10: decimal

A majority of traditional number systems are based on the decimal numeral system. Anthropologists hypothesize this may be due to humans having five fingers per hand, ten in total. There are many regional variations including:

Historically, its use was first employed by the ancient Egyptians, who invented a wholly decimal system, and later extended by the Babylonians and also a system of pictorial representation, substituting letters and other reminders with symbols.English farmer coined the term notch: defined as ten. from the tally sticks of the livestock- a full deep score for every twenty, a half score or notch pret half score- or ten.

12: duodecimal

Duodecimal numbers or systems based around the base unit of 12, are a frequent occurrence.

These include:

Duodecimal numeric system have some practical advantages over decimal. It is much easier to divide the base digit twelve (which is a highly composite number) by many important divisors in market and trade settings, such as the numbers 2, 3, 4 and 6. It is still common usage and is found in idiom. For example, "A dime a dozen" refers to something so common or numerous as to be of little worth or noteworthiness.

The system of basing counting on the number 12, is widespread, across many cultures.Examples include:
  • time divisions (twelve months in a year, the twelve-hour clock)
  • measurement imperial system of units (twelve inches to the foot, twelve Troy ounces to the Troy pound)
  • traditional British monetary system (twelve pence to the shilling)

Consequently, languages evolved or loaned terms such dozen, gross and great gross, which allow for rudimentary and arguably immediately comprehensible duodecimal nomenclature (e.g., stating: "two gross and six dozen" instead of "three hundred and sixty"). Ancient Romans used decimal for integers, but switched to duodecimal for fractions, and correspondingly Latin developed a rich vocabulary for duodecimal-based fractions (see Roman numerals). A notably novel and invented system of duodecimal was J. R. R. Tolkien's Elvish languages who used duodecimal as well as decimal.

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 combinedThe system is in widespread use across the world. Some include the classical Mesoamerican cultures, still in use today in the modern indigenous languages of their descendants, namely the Nahuatl and Mayan languages (see also Maya numerals).Vigesimal terminology is also found in some European languages: Basque, Celtic languages, French (from Celtic languages), Danish and Georgian.The term score originates from tally sticks, where taxmen and farmers would groove a notch for every ten, and a full score for every twenty.The English term score, now rarely used, is a remnant of vigesimal numeration in the word score. It was widely used to learn the pre-decimal British currency in this idiom: "a dozen pence and a score of bob" , referring to the 20 shillings in a pound_sterling. For Americans the term is most known from the opening of the Gettysburg Address: "Four score and seven years ago, our Forefathers...".

For very large (and very small) numbers, traditional systems have been superseded by the use of scientific notation and the system of SI prefixes. Traditional systems continue to be used in everyday life.

Numeral symbols

The numbers one through ten in different numeral systems
Arabic ١ ٢ ٣ ٤ ٥ ٦ ٧ ٨ ٩ ١٠
Bangla (Bengali) ১০
Devanagari १०
Classical Greek (note: all written - above letters) α β γ δ ε ζ η θ ι κ
Hebrew א ב ג ד ה ו ז ח ט י
West Arabic 1 2 3 4 5 6 7 8 9 10
Malayalam ൧൦
Phoenician A B Δ E ζ Z H θ I
Suzhou 〡〇
Thai ๑๐

Counting aids

Counting aids, especially the use of body parts (counting on fingers), were certainly used in prehistoric times as today. There are many variations. Besides counting 10 fingers, some cultures have counted knuckles, the space between fingers, and toes as well as fingers. The Oksapmin culture of New Guinea uses a system of 27 upper body locations to represent numbers.

To preserve numerical information, tallies carved in wood, bone, and stone have been used since prehistoric times. Stone age cultures, including ancient American Indian groups, used tallies for gambling, personal services, and trade-goods.

A method of preserving numeric information in clay was invented by the Sumerians between 8000 and 3500 BCE. This was done with small clay tokens of various shapes that were strung like beads on a string. Beginning about 3500 BCE clay tokens were gradually replaced by number signs impressed with a round stylus at different angles in clay tablets (originally containers for tokens) which were then baked. About 3100 BCE written numbers were dissociated from the things being counted and became abstract numerals.

Between 2700 BCE and 2000 BCE in Sumer, the round stylus was gradually replaced by a reed stylus that was used to press wedge-shaped cuneiform signs in clay. These cuneiform number signs resembled the round number signs they replaced and retained the additive sign-value notation of the round number signs. These systems gradually converged on a common sexagesimal number system; this was a place-value system consisting of only two impressed marks, the vertical wedge and the chevron, which could also represent fractions. This sexagesimal number system was fully developed at the beginning of the Old Babylonia period (about 1950 BC) and became standard in Babylonia.

Sexagesimal numerals were a mixed radix system that retained the alternating base 10 and base 6 in a sequence of cuneiform vertical wedges and chevrons. By 1950 BCE this was a positional notation system. Sexagesimal numerals came to be widely used in commerce, but were also used in astronomical and other calculations. This system was exported from Babylonia and used throughout Mesopotamia, and by every Mediterranean nation that used standard Babylonian units of measure and counting, including the Greeks, Romans and Egyptians. Babylonian-style sexagesimal numeration is still used in modern societies to measure time (minutes per hour) and angles (degrees).

In Chinamarker, armies and provisions were counted using modular tallies of prime numbers. Unique numbers of troops and measures of rice appear as unique combinations of these tallies. A great convenience of modular arithmetic is that it is easy to multiply, though quite difficult to add. This makes use of modular arithmetic for provisions especially attractive. Conventional tallies are quite difficult to multiply and divide. In modern times modular arithmetic is sometimes used in Digital signal processing.

The oldest Greek system was the that of the Attic numerals, but in the 4th century BC they began to use a quasidecimal alphabetic system (see Greek numerals). Jews began using a similar system (Hebrew numerals), with the oldest examples known being coins from around 100 BC.

The Roman empire used tallies written on wax, papyrus and stone, and roughly followed the Greek custom of assigning letters to various numbers. The Roman numerals system remained in common use in Europe until positional notation came into common use in the 1500s.

The Maya of Central America used a mixed base 18 and base 20 system, possibly inherited from the Olmec, including advanced features such as positional notation and a zero. They used this system to make advanced astronomical calculations, including highly accurate calculations of the length of the solar year and the orbit of Venus.

The Incan Empire ran a large command economy using quipu, tallies made by knotting colored fibers. Knowledge of the encodings of the knots and colors was suppressed by the Spanishmarker conquistadors in the 16th century, and has not survived although simple quipu-like recording devices are still used in the Andean region.

Some authorities believe that positional arithmetic began with the wide use of counting rods in China. The earliest written positional records seem to be rod calculus results in China around 400. In particular, zero was correctly described by Chinese mathematicians around 932.

The modern positional Arabic numeral system was developed by mathematicians in India, and passed on to Muslim mathematicians, along with astronomical tables brought to Baghdadmarker by an Indian ambassador around 773.

From Indiamarker, the thriving trade between Islamic sultans and Africa carried the concept to Cairomarker. Arabic mathematicians extended the system to include decimal fractions, and wrote an important work about it in the 9th century. The modern Arabic numerals were introduced to Europe with the translation of this work in the 12th century in Spain and Leonardo of Pisa's Liber Abaci of 1201. In Europe, the complete Indian system with the zero was derived from the Arabs in the 12th century.{{citation]]

The binary system (base 2), was propagated in the 17th century by Gottfried Leibniz. Leibniz had developed the concept early in his career, and had revisited it when he reviewed a copy of the I ching from China. Binary numbers came into common use in the 20th century because of computer applications.

Numerals in most popular systems

West Arabic 0 1 2 3 4 5 6 7 8 9
East Arabic ٠ ١ ٢ ٣ ٤ ٥ ٦ ٧ ٨ ٩
Asomiya (Assamese)


贰/貳 叁/叄 陆/陸


Urdu ۰ ۱ ۲ ۳ ۴ ۵ ۶ ۷ ۸ ۹

Additional numerals

10 20 30 40 100 1000 10000 108 1012

廿 亿


10 20 30 40 50 60 70 80 90 100 10000


10 50 100 500 1000

See also

Numerals in various languages

Numeral notation in various scripts

Related topics


  1. LinguaLinks Library
  3. Hammarström (2006) "Rarities in numeral systems"
  4. Ryan, Peter. Encyclopaedia of Papua and New Guinea. Melbourne University Press & University of Papua and New Guinea,:1972 ISBN 0522840256.: 3 pages pp219.
  5. Aleksandr Romanovich Luriicac, Lev Semenovich Vygotskiĭ, Evelyn Rossiter. Ape, primitive man, and child: essays in the history of behavior . CRC Press: 1992: ISBN 1878205439: 171 pages
  6. Heath, Thomas, A Manual of Greek Mathematics, Courier Dover: 2003. ISBN 0486432319 576 page, p:11
  7. Georges Ifrah, The Universal History of Numbers: The Modern Number System, Random House, 2000: ISBN 1860467911: 1262 pages
  8. Scientific American Munn& Co: 1968, vol 219: 219
  9. Karl Menninger, Paul Broneer, Number Words and Number Symbols Courier Dover Publications: 1992: ISBN 0486270963: 480 pages

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