quinary

Many languages{{Cite book |last=Hammarström |first=Harald |url=https://www.degruyter.com/document/doi/10.1515/9783110220933.11/html |title=Rethinking Universals |date=March 26, 2010 |publisher=De Gruyter Mouton |isbn=9783110220933 |volume=45 |pages=11–60 |chapter=Rarities in numeral systems |doi=10.1515/9783110220933.11 |access-date=May 14, 2023 |url-access=registration }} use quinary number systems, including Gumatj, Nunggubuyu,{{Cite web |last=Harris |first=John W. |date=December 1982 |others=Work Papers of SIL-AAB |title=Facts and fallacies of Aboriginal number system |url=http://www1.aiatsis.gov.au/exhibitions/e_access/serial/m0029743_v_a.pdf |url-status=dead |archive-url=https://web.archive.org/web/20070831202737/http://www1.aiatsis.gov.au/exhibitions/e_access/serial/m0029743_v_a.pdf |archive-date=August 31, 2007 |access-date=May 14, 2023 |website=www1.aiatsis.gov.au |pages=153–181 }} Kuurn Kopan Noot,{{Cite book |last=Dawson |first=James |url=https://archive.org/details/australianabori00dawsgoog |title=Australian aborigines : the languages and customs of several tribes of aborigines in the western district of Victoria, Australia |publisher=Canberra City, ACT, Australia : Australian Institute of Aboriginal Studies; Atlantic Highlands, NJ : Humanities Press [distributor] |others=University of Michigan |year=1981 |access-date=May 14, 2023}} Luiseño,{{Cite book |author-last=Closs |author-first=Michael P. |title=Native American Mathematics |year=1986 |isbn=0-292-75531-7}} 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).

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

File:Chinese-abacus.jpg

A decimal system with two and five as a sub-bases is called biquinary and is found in Wolof and Khmer. Roman numerals 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, 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 IBM 650 to represent decimal numbers.

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.

• {{annotated link|Pentadic numerals}}
• Bi-quinary coded decimal

{{reflist|refs=

{{cite web |url=http://www.sharp-world.com/contents/calculator/support/guidebook/pdf/OperationGuide_ELW531.pdf |title=SHARP |access-date=2017-06-05 |url-status=live |archive-url=https://web.archive.org/web/20170712182220/http://www.sharp-world.com/contents/calculator/support/guidebook/pdf/OperationGuide_ELW531.pdf |archive-date=2017-07-12 }}

{{cite web |url=http://www.sharp.de/cps/rde/xbcr/documents/documents/om/30_cal/ELW506-W516-W546_OM_DE.pdf |title=Archived copy |access-date=2017-06-05 |url-status=live |archive-url=https://web.archive.org/web/20160222014019/http://www.sharp.de/cps/rde/xbcr/documents/documents/om/30_cal/ELW506-W516-W546_OM_DE.pdf |archive-date=2016-02-22 }}

{{cite web |url=http://www.sharp-world.com/contents/calculator/support/guidebook/pdf/scientific_calculator_operation_guide.pdf |title=SHARP |access-date=2017-06-05 |url-status=live |archive-url=https://web.archive.org/web/20170712124336/http://www.sharp-world.com/contents/calculator/support/guidebook/pdf/scientific_calculator_operation_guide.pdf |archive-date=2017-07-12 }}

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• [http://www.mathsisfun.com/numbers/convert-base.php?to=quinary Quinary Base Conversion], includes fractional part, from Math Is Fun
• {{commons category-inline|Quinary numeral system}}
• [http://www.florestica.com/hpotd/dni_calculator/index.html Quinary-pentavigesimal and decimal calculator], uses D'ni numerals from the Myst franchise, integers only, fan-made.

Category:Positional numeral systems

Category:5 (number)