Quinary

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Quinary (base-5) is a numeral system with five as the base. A possible origination of a quinary system is that there are five fingers on either hand.

In the quinary place system, five numerals from 0 to 4, are used to represent any real number. According to this method, five is written as 10, twenty-five is written as 100 and sixty is written as 220.

Usage

Many languages^[1] use quinary number systems, including Gumatj, Nunggubuyu,^[2], Kuurn Kopan Noot^[3] and Saraveca. Of these, Gumatj is the only true "5-25" language known, in which 25 is the higher group of 5. The Gumatj numerals are shown below:

A decimal system with 5 as a sub-base is called biquinary, and is found in Wolof and Khmer. A vigesimal system with 5 as a sub-base is found in Nahuatl and the Maya numerals.

Roman numerals are a biquinary system. The numbers 1, 5, 10, and 50 are written as I, V, X, and L respectively. Eight is VIII and seventy is LXX.

The Chinese and Japanese versions of the abacus use a biquinary system to simulate a decimal system for ease of calculation.

Urnfield culture numerals and some tally mark systems are also biquinary.

Units of currencies are commonly partially or wholly biquinary.

References

1. ^ Harald Hammarström, Rarities in Numeral Systems: "Bases 5, 10, and 20 are omnipresent."
2. ^ Harris, John (1982), Hargrave, Susanne, ed., "Facts and fallacies of aboriginal number systems", Work Papers of SIL-AAB Series B 8: 153–181, http://www1.aiatsis.gov.au/exhibitions/e_access/serial/m0029743_v_a.pdf 
3. ^ Dawson, J. "Australian Aborigines: The Languages and Customs of Several Tribes of Aborigines in the Western District of Victoria (1881), p. xcviii.

See also

• Pentimal system
• Quibinary
• Yan Tan Tethera

External links

• Quinary Base Conversion, includes fractional part, from Math Is Fun

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