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

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. 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. As five is a prime number, only the reciprocals of the powers of five terminate, although its location between two highly composite numbers ( 4 and 6) guarantees that many recurring fractions have relatively short periods.

Comparison to other radices

Usage

Many languages use quinary number systems, including Gumatj, Nunggubuyu, Kuurn Kopan Noot, Luiseño, and Saraveca. Gumatj has been reported to be a true "5–25" language, in which 25 is the higher group of 5. The Gumatj numerals are shown below: However, Harald Hammarström reports that "one would not usually use exact numbers for counting this high in this language and there is a certain likelihood that the system was extended this high only at the time of elicitation with one single speaker," pointing to the Biwat language as a similar case (previously attested as 5-20, but with one speaker recorded as making an innovation to turn it 5-25).

Biquinary

: ''In this section, the numerals are in decimal. For example, "5" means five, and "10" means ten.'' Chinese-abacus

A decimal system with two and five as a sub-bases is called biquinary and is found in Wolof and Khmer.

Roman numeral 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, ea ...

s are an early biquinary system. The numbers 1, 5, 10, and 50 are written as I, V, X, and L respectively. Seven is VII, and seventy is LXX. The full list of symbols is: Note that these are not positional number systems. In theory, a number such as 73 could be written as IIIXXL (without ambiguity) and as LXXIII. To extend Roman numerals to beyond thousands, a vinculum (horizontal overline) was added, multiplying the letter value by a thousand, e.g. overlined M̅ was one million. There is also no sign for zero. But with the introduction of inversions like IV and IX, it was necessary to keep the order from most to least significant. Many versions of the abacus, such as the suanpan and

soroban The is an abacus developed in Japan. It is derived from the History of Science and Technology in China, ancient Chinese suanpan, imported to Japan in the 14th century. Like the suanpan, the soroban is still used today, despite the proliferation ...

, 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. Bi-quinary coded decimal is a variant of biquinary that was used on a number of early computers including Colossus and the

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to represent decimal numbers.

Calculators and programming languages

Few calculators support calculations in the quinary system, except for some Sharp models (including some of the EL-500W and EL-500X series, where it is named the ''pental system'') since about 2005, as well as the open-source scientific calculator WP 34S.

References

External links

Quinary Base Conversion
includes fractional part, from Math Is Fun * {{commons category-inline, Quinary numeral system

uses D'ni numerals from the

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