Some theories of grammar use the word "numeral" to refer to cardinal numbers that act as a determiner that specify the quantity of a noun, for example the "two" in "two hats".
Some theories of grammar do not include determiners as a part of speech and consider "two" in this example to be an adjective.
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.
In English grammar, the classification "numeral" (viewed as a part of speech) is reserved for those words which have distinct grammatical behavior: when a numeral modifies a noun, it may replace the article: the/some dogs played in the park → twelve dogs played in the park.
In linguistics, however, numerals are classified according to purpose: examples are ordinal numbers (first, second, third, etc.
Georgian,[4] Latin, and Romanian (see Romanian distributive numbers) have regular distributive numbers, such as Latin singuli "one-by-one", bini "in pairs, two-by-two", terni "three each", etc.
The Mesoamerican system, still used to some extent in Mayan languages, was based on powers of 20: bak’ 400 (202), pik 8000 (203), kalab 160,000 (204), etc.
This table compares the English names of cardinal numbers according to various American, British, and Continental European conventions.
There is no consistent and widely accepted way to extend cardinals beyond centillion (centilliard).
[14] Many languages of Melanesia have (or once had) counting systems based on parts of the body which do not have a numeric base; there are (or were) no numerals, but rather nouns for relevant parts of the body—or simply pointing to the relevant spots—were used for quantities.
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.
Ternary systems are based on the number 3, having practical usage in some analog logic, in baseball scoring and in self–similar mathematical structures.
Some Austronesian, Melanesian, Sulawesi, and Papua New Guinea ethnic groups, count with the base number four, using the term asu or aso, the word for dog, as the ubiquitous village dog has four legs.
The Morehead-Maro languages of Southern New Guinea are examples of the rare base 6 system with monomorphemic words running up to 66.
The Sko languages on the North Coast of New Guinea follow a base-24 system with a sub-base of 6.
Septenary systems are very rare, as few natural objects consistently have seven distinctive features.
Anthropologists hypothesize this may be due to humans having five digits per hand, ten in total.
Ancient Romans used a decimal system for integers, but switched to duodecimal for fractions, and correspondingly Latin developed a rich vocabulary for duodecimal-based fractions (see Roman numerals).
The suanpan (Chinese abacus) can be used to perform hexadecimal calculations such as additions and subtractions.
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.
A modern national language which uses a full vigesimal system is Dzongkha in Bhutan.
The term score originates from tally sticks, and is perhaps a remnant of Celtic vigesimal counting.
It was widely used to learn the pre-decimal British currency in this idiom: "a dozen pence and a score of bob", referring to the 20 shillings in a pound.
For Americans the term is most known from the opening of the Gettysburg Address: "Four score and seven years ago our fathers...".
Sumeria had a base-60 system with a decimal sub-base (with alternating cycles of 10 and 6), which was the origin of the numbering of modern degrees, minutes, and seconds.
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).
Chan of Hong Kong is hosted by the Max Planck Institute for Evolutionary Anthropology in Leipzig, Germany.