Quinary (base 5 or pental) is a

numeral system A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. The same sequence of symbols may represent differe ...

with five as the base. A possible origination of a quinary system is that there are five digits on either

hand A hand is a prehensile, multi-fingered appendage located at the end of the forearm or forelimb of primates such as humans, chimpanzees, monkeys, and lemurs. A few other vertebrates such as the Koala#Characteristics, koala (which has two thumb#O ...

. In the quinary place system, five numerals, from 0 to 4, are used to represent any

real number In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every re ...

. 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 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''(' ...

s ( 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 The Yolngu or Yolŋu ( or ) are an aggregation of Aboriginal Australian people inhabiting north-eastern Arnhem Land in the Northern Territory of Australia. ''Yolngu'' means "person" in the Yolŋu languages. The terms Murngin, Wulamba, Yalnum ...

, Nunggubuyu, Kuurn Kopan Noot,

Luiseño The Luiseño or Payómkawichum are an Indigenous people of California who, at the time of the first contacts with the Spanish in the 16th century, inhabited the coastal area of southern California, ranging from the present-day southern part of ...

, and

Saraveca Saraveca is an extinct Arawakan language once spoken in Bolivia by the Sarave. By 1962, most people has switched to Chiquitano. Numbers It is said to be the only language with a numeral system based exclusively on five, although quinary syst ...

. 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

decimal The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (''decimal fractions'') of th ...

system with two and five as a sub-bases is called

biquinary Bi-quinary coded decimal is a numeral encoding scheme used in many abacuses and in some early computers, notably the Colossus. The term ''bi-quinary'' indicates that the code comprises both a two-state (''bi'') and a five-state (''quin'' ...

and is found in

Wolof Wolof or Wollof may refer to: * Wolof people, an ethnic group found in Senegal, Gambia, and Mauritania * Wolof language, a language spoken in Senegal, Gambia, and Mauritania * The Wolof or Jolof Empire, a medieval West African successor of the Mal ...

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 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 ...

, such as the

suanpan The suanpan (), also spelled suan pan or souanpan) is an abacus of Chinese origin, earliest first known written documentation of the Chinese abacus dates to the 2nd century BCE during the Han dynasty, and later, described in a 190 CE book of ...

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 Tally marks, also called hash marks, are a form of numeral used for counting. They can be thought of as a unary numeral system. They are most useful in counting or tallying ongoing results, such as the score in a game or sport, as no interm ...

systems are also biquinary. Units of

currencies A currency is a standardization of money in any form, in use or currency in circulation, circulation as a medium of exchange, for example banknotes and coins. A more general definition is that a currency is a ''system of money'' in common use wi ...

are commonly partially or wholly biquinary.

Bi-quinary coded decimal Bi-quinary coded decimal is a numeral encoding scheme used in many abacuses and in some early computers, notably the Colossus. The term ''bi-quinary'' indicates that the code comprises both a two-state (''bi'') and a five-state (''quin''a ...

is a variant of biquinary that was used on a number of early computers including

Colossus Colossus, Colossos, or the plural Colossi or Colossuses, may refer to: Statues * Any exceptionally large statue; colossal statues, are generally taken to mean a statue at least twice life-size ** List of tallest statues ** :Colossal statues * ...

and the

IBM 650 The IBM 650 Magnetic Drum Data-Processing Machine is an early digital computer produced by IBM in the mid-1950s. It was the first mass-produced computer in the world. Almost 2,000 systems were produced, the last in 1962, and it was the firs ...

to represent decimal numbers.

Calculators and programming languages

Few

calculator An electronic calculator is typically a portable electronic device used to perform calculations, ranging from basic arithmetic to complex mathematics. The first solid-state electronic calculator was created in the early 1960s. Pocket-si ...

s 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 ''Myst'' is a franchise centered on a series of adventure game, adventure video games. The first game in the series, ''Myst'', was released in 1993 by brothers Rand Miller, Rand and Robyn Miller and their video game company Cyan Worlds, Cyan, In ...

numerals from the

Myst ''Myst'' is a 1993 adventure video game developed by Cyan and published by Broderbund for Mac OS. In the game, the player travels via a special book to a mysterious island called Myst. The player interacts with objects and traverses the ...