Editing Decimal separator (section)

==History==
===Hellenistic–Renaissance eras===
{{anchor|Separatrix|Pythagorean arc}}
In the [[Middle Ages]], before printing, a [[overline|bar]] ( ¯ ) over the [[units digit]] was used to separate the integral part of a number from its [[fractional part]], as in 9{{overline|9}}95 (meaning 99.95 in [[decimal]] point format). A similar notation remains in common use as an underbar to superscript digits, especially for monetary values without a decimal separator, as in 99<sup>{{underline|95}}</sup>. Later, a "separatrix" (i.e., a short, roughly vertical ink stroke) between the units and tenths position became the norm among [[Mathematics in medieval Islam|Arab mathematicians]] (e.g. 99'''ˌ'''95), while an L-shaped or [[vertical bar]] ({{!}}) served as the separatrix in England.<ref>{{cite dictionary |dictionary=Oxford English Dictionary |title=separatrix, ''n.'' |place=Oxford, UK |publisher=Oxford University Press }}</ref> When this character was [[typeset]], it was convenient to use the existing [[Comma (punctuation)|comma]] (99''','''95) or [[full stop]] (99'''.'''95) instead.

Positional [[decimal fraction]]s appear for the first time in a book by the Arab mathematician [[Abu'l-Hasan al-Uqlidisi]] written in the 10th century.<ref name=Berggren>{{cite book |first=J. Lennart |last=Berggren |year=2007 |chapter=Mathematics in Medieval Islam |editor-first=Victor J. |editor-last=Katz |title=The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A sourcebook |publisher=Princeton University Press |isbn=978-0-691-11485-9 |page=530 }}</ref> The practice is ultimately derived from the decimal [[Hindu–Arabic numeral system]] used in [[Indian mathematics]],<ref>{{cite book |author1=Reimer, L. |author2=Reimer, W. |title=Mathematicians are People, too: Stories from the lives of great mathematicians |volume=2 |year=1995 |pages=22 |place=Parsippany, NJ |publisher=Pearson Education, / Dale Seymor Publications |isbn=0-86651-823-1}}</ref> and popularized by the [[Persian people|Persian]] mathematician [[Al-Khwarizmi]],<ref>{{cite web |url=http://www.oxfordislamicstudies.com/article/opr/t125/e1305 |archive-url=https://web.archive.org/web/20130618081123/http://www.oxfordislamicstudies.com/article/opr/t125/e1305 |url-status=dead |archive-date=18 June 2013 |title=Khwarizmi, Abu Jafar Muhammad ibn Musa al- |type=biography |website=Oxford Islamic Studies Online}}</ref> when [[Latin]] translation of [[#Arithmetic|his work]] on the [[Indian numerals]] introduced the decimal [[Positional notation|positional number system]] to the Western world. His ''[[Compendious Book on Calculation by Completion and Balancing]]'' presented the first systematic solution of [[linear equation|linear]] and [[quadratic equation]]s in Arabic.

[[Pope Sylvester II|Gerbert of Aurillac]] marked triples of columns with an arc (called a "Pythagorean arc"), when using his Hindu–Arabic numeral-based abacus in the 10th&nbsp;century. [[Fibonacci]] followed this convention when writing numbers, such as in his influential work {{lang|la|[[Liber Abaci]]}} in the 13th&nbsp;century.<ref>{{cite book |last=Devlin |first=Keith |year=2011 |title=The Man of Numbers: Fibonacci's Arithmetic Revolution |publisher=Walker & Company |place=New York, NY |isbn=9780802779083 |pages=[https://archive.org/details/manofnumbersfibo0000devl/page/44 44–45] |url=https://archive.org/details/manofnumbersfibo0000devl |url-access=registration }}</ref> 

The earliest known record of using the decimal point is in the astronomical tables compiled by the Italian merchant and mathematician [[Giovanni Bianchini]] in the 1440s.<ref>{{Cite journal |last=Marchant |first=Jo |date=2024-02-19 |title=The decimal point is 150 years older than historians thought |url=https://www.nature.com/articles/d41586-024-00473-2 |journal=Nature |language=en |doi=10.1038/d41586-024-00473-2|pmid=38374392 |url-access=subscription }}</ref>{{contradict-inline|History of mathematical notation#Indian and Arabic numerals and notation|date=April 2025}}

Tables of [[logarithm]]s prepared by [[John Napier]] in 1614 and 1619 used the period (full stop) as the decimal separator, which was then adopted by [[Henry Briggs (mathematician)|Henry Briggs]] in his influential 17th century work.

In [[France]], the full stop was already in use in printing to make [[Roman numerals]] more readable, so the comma was chosen.<ref name=Santillana-1996>{{cite encyclopedia |encyclopedia=Enciclopedia Universal Santillana |year=1996 |publisher=Santillana S.A. |place=Barcelona, Spain |isbn=84-294-5129-3 |title=Comma |at=def.&nbsp;2 |quote=coma: MAT. Signo utilizado en los números no enteros para separar la parte entera de la parte decimal o fraccionaria; p.&nbsp;ej., {{nobr| 2,123 .}} }}</ref>

Many other countries, such as Italy, also chose to use the comma to mark the decimal units position.<ref name=Santillana-1996/> It has been [[ISO 80000-2|made standard]] by the [[International Organization for Standardization|ISO]] for international blueprints.<ref>{{cite report |title=Quantities and units |section=Part&nbsp;2: Mathematical signs and symbols to be used in the natural sciences and technology |id=ISO 80000-2:2009 |year=2009 |publisher=[[International Organization for Standardization]] |section-url=http://www.iso.org/iso/catalogue_detail?csnumber=31887 |access-date=1 July 2010}}</ref> However, English-speaking countries took the comma to separate sequences of three digits. In some countries, a raised dot or dash (''{{visible anchor|upper comma}}'') may be used for grouping or decimal separator; this is particularly common in handwriting.

===English-speaking countries===
In the [[United States]], the full stop or period (.) is used as the standard decimal separator.

[[File:Interpunct as decimal point in Henderson 1839.png|thumb|upright=1.8|The [[interpunct]] (·) used as a decimal separator in a British print from 1839<ref>for example: {{cite journal |author=Henderson, Thomas |date=1839-01-03 |title=On the parallax of {{mvar|α}}&nbsp;Centauri |journal=[[Memoirs of the Royal Astronomical Society]] |volume=11 |pages=61–64, esp.&nbsp;64 |bibcode=1840MmRAS..11...61H |via=scan published by [[Harvard-Smithsonian Center for Astrophysics]] }}</ref>]]
In the nations of the [[British Empire]] (and, later, the [[Commonwealth of Nations]]), the full stop could be used in typewritten material and its use was not banned, although the [[interpunct]] (a.k.a. decimal point, point or mid dot) was preferred as a decimal separator, in printing technologies that could accommodate it, e.g. {{nobr| 99·95 .}}<ref>{{cite book |author1=Reimer, L. |author2=Reimer, W. |year=1990 |title=Mathematicians are People, too: Stories from the lives of great mathematicians |volume=1 |page=41 |place=Parsippany, NJ |publisher=Pearson Education / Dale Seymor Publications |isbn=0-86651-509-7}}</ref> However, as the mid dot was already in common use in the mathematics world to indicate multiplication, the [[SI]] rejected its use as the decimal separator.

During the beginning of British [[metrication]] in the late 1960s and with impending currency [[decimalisation]], there was some debate in the United Kingdom as to whether the decimal comma or decimal point should be preferred: the [[British Standards Institution]] and some sectors of industry advocated the comma and the [[Decimal Day|Decimal Currency Board]] advocated for the point. In the event, the point was chosen by the [[Ministry of Technology]] in 1968.<ref>{{cite journal | title = Victory on points | year = 1968 | journal = Nature | volume = 218 | issue = 5137 | page = 111 | bibcode = 1968Natur.218S.111. | doi = 10.1038/218111c0 | doi-access = free}}</ref>

[[File:MUTCD-CA G11-6.svg|thumb|right|upright|x180px|California milepost marker at mile 144.44]]
When South Africa [[metrication|adopted the metric system]], it adopted the comma as its decimal separator,<ref>{{cite periodical |title=Government Notice R.&nbsp;1144 |periodical=Government Gazette |issue=4326 |date=5 July 1974 |page=55 |url=https://laws.parliament.na/cms_documents/gg-4326-a7726e51e7.pdf|archive-url=https://web.archive.org/web/20210308203659/https://laws.parliament.na/cms_documents/gg-4326-a7726e51e7.pdf |archive-date=8 March 2021 }}</ref> although a number of house styles, including some English-language newspapers such as ''[[Sunday Times (South Africa)|The Sunday Times]]'', continue to use the full stop.{{citation needed|date=January 2015}}

Previously, signs along [[California]] roads expressed distances in decimal numbers with the decimal part in superscript, as in 3<sup><u>7</u></sup>, meaning 3.7.<ref>{{cite magazine|title=Signposts: Directions for the Traveler Are Hundreds of Years Old|first=George M.|last=Webb|work=[[California Highways and Public Works]]|location=Sacramento, California|publisher=California Division of Highways|volume=35|issue=5–6|date=May–June 1956|page=11|url=https://libraryarchives.metro.net/dpgtl/californiahighways/chpw_1956_mayjun.pdf#page=13}}</ref> Though California has since transitioned to [[mixed number]]s with [[common fraction]]s, the older style remains on [[California postmile|postmile]] markers and bridge inventory markers.

===Constructed languages===
The three most spoken [[international auxiliary language]]s, [[Ido]], [[Esperanto]], and [[Interlingua]], all use the comma as the decimal separator.

Interlingua has used the comma as its decimal separator since the publication of the [[Interlingua: A Grammar of the International Language|Interlingua Grammar]] in 1951.<ref>{{cite web |series=Grammar of Interlingua |title=Parts of Speech – Numerals |url=http://members.optus.net/~ado_hall/interlingua/gi/parts_of_speech/numerals.html |access-date=2008-03-18 |url-status=dead |archive-url=http://arquivo.pt/wayback/20160516201404/http://members.optus.net/~ado_hall/interlingua/gi/parts_of_speech/numerals.html |archive-date=2016-05-16}}</ref>

Esperanto also uses the comma as its official decimal separator, whilst thousands are usually separated by [[non-breaking space]]s (e.g. {{nobr|12 345 678,9}}). It is possible to separate thousands by a [[full stop]] (e.g. {{nobr|12.345.678,9}}), though this is not as common.<ref>{{cite book |last1=Wennergren |first1=Bertilo |title=Plena Manlibro de Esperanta Gramatiko |trans-title=Complete Manual of Esperanto Grammar |chapter=Helposignoj |trans-chapter=Helping Symbols |edition=15.4 |url=https://bertilow.com/pmeg/ |chapter-url=https://bertilow.com/pmeg/skribo_elparolo/skribo/helposignoj.html |date=5 July 2023 |lang=Esperanto}}</ref>

Ido's ''Kompleta Gramatiko Detaloza di la Linguo Internaciona Ido'' (Complete Detailed Grammar of the International Language Ido) officially states that commas are used for the decimal separator whilst full stops are used to separate thousands, millions, etc. So the number 12,345,678.90123 (in American notation), for instance, would be written ''12.345.678,90123'' in Ido.

The 1931 grammar of [[Volapük]] uses the comma as its decimal separator but, somewhat unusually, the middle dot as its thousands separator (12·345·678,90123).<ref>{{cite book |author=de&nbsp;Jong, Arie |author-link=Arie de Jong |year=2012 |title=Gramat Volapüka. Cathair na Mart |editor=Everson, Michael |publisher=Evertype |isbn=978-1-904808-94-7 |url=http://evertype.com/books/dejong-gramat.html}}</ref>

In 1958, disputes between European and American delegates over the correct representation of the decimal separator nearly stalled the development of the [[ALGOL]] computer programming language.<ref>Perlis, Alan, ''The American Side of the Development of ALGOL'', ACM SIGPLAN Notices, August 1978.</ref> ALGOL ended up allowing different decimal separators, but most computer languages and standard data formats (e.g., [[C (programming language)|C]], [[Java (programming language)|Java]], [[Fortran]], [[CSS|Cascading Style Sheets (CSS)]]) specify a dot. [[C++14#Digit_separators|C++]] and a couple of others permit a quote (') as thousands separator, and many others like Python and Julia, (only) allow '_' as such a separator (it's usually ignored, i.e. also allows 1_00_00_000 aligning with the Indian number style of 1,00,00,000 that would be 10,000,000 in the US).

=== Radix point ===
In mathematics and [[computing]], a '''radix point''' or '''radix character''' is a symbol used in the display of numbers to separate the [[integer]] part of the value from its [[fractional part]]. In English and many other languages (including many that are written right-to-left), the integer part is at the left of the radix point, and the fraction part at the right of it.<ref>{{cite book |last1=Van Verth |first1=James M. |last2=Bishop |first2=Lars M. |year=2008 |title=Essential Mathematics for Games and Interactive Applications: A programmers' guide |edition=2nd |place=Boca Raton, Florida |publisher=CRC Press |page=7 |isbn=9780123742971 |url=https://books.google.com/books?id=zkEY9RIm4WkC&pg=PA7}}</ref>

A radix point is most often used in [[decimal]] (base 10) notation, when it is more commonly called the ''decimal point'' (with [[wiktionary:deci-|deci-]] indicating [[base&nbsp;10]]). In [[List of countries where English is an official language|English-speaking countries]], the decimal point is usually a small dot (.) placed either on the baseline, or halfway between the baseline and the top of the [[Numerical digit|digits]] ('''·''')<ref name=oracle>{{cite report |title=International Language Environments Guide |url=https://docs.oracle.com/cd/E19455-01/806-0169/overview-9/index.html |archive-url=https://web.archive.org/web/20120115042427/https://docs.oracle.com/cd/E19455-01/806-0169/overview-9/index.html|archive-date=2012-01-15 |access-date=2018-12-19 |website=[[Oracle Corporation|Oracle Corporation Docs]] |df=dmy-all}}</ref>{{efn|name=oracle_quote|Great Britain and the United States are two of the few places in the world that use a period to indicate the decimal place. Many other countries use a comma instead. The decimal separator is also called the ''radix'' character. Likewise, while the U.K. and U.S. use a comma to separate groups of thousands, many other countries use a period instead...<ref name=oracle/>}}
In many other countries, the radix point is a comma (,) placed on the baseline.<ref name=oracle/>{{efn|name=oracle_quote}}

These conventions are generally used both in machine displays ([[printing]], [[computer monitor]]s) and in [[handwriting]]. It is important to know which notation is being used when working in different software programs. The respective [[ISO 31-0#Numbers|ISO 31-0 standard]] defines both the comma and the small dot as decimal markers, but does not explicitly define universal radix marks for bases other than 10.

Fractional numbers are rarely displayed in other [[Radix|number bases]], but, when they are, a radix character may be used for the same purpose. When used with the [[Binary number|binary]] (base&nbsp;2) representation, it may be called "binary point".