Decimal separator: Difference between revisions

Content deleted Content added
Rescuing 2 sources and tagging 0 as dead.) #IABot (v2.0.9.5) (AManWithNoPlan - 15323
No edit summary
 
(65 intermediate revisions by 54 users not shown)
Line 1:
{{Short description|Numerical symbol}}
{{For|decimal separator use in Wikipedia articles|Wikipedia:Manual of Style (dates and numbers)#Decimal points|selfref=true}}{{useUse dmy dates|date=November 2022}}
{{Redirect|Decimal period|the period of a repeating decimal fraction|Repeating decimal}}
 
{{Numeral systems}}
[[File:Common_decimal_separators_-_Decimal_point_and_decimal_comma.png|thumb|right|Both a [[comma]] and a [[full stop|period]] (or full-stop) are generally accepted decimal separators for international use.]]
[[File:Thousands separators.gif|thumb|Three ways to group the number ten thousand with digit group separators.<br/>1) Space, the internationally recommended thousands separator.<br/>2) Period (or full stop), the thousands separator used in many non-English speaking countries.<br/>3) Comma, the thousands separator used in most English-speaking countries.]]
{{Cleanup|Conventions worldwide, Examples of use|reason=Use by region is inconsistent, inaccurate, and are poorly formatted.|date=March 2023}}
A '''decimal separator''' is a symbol used to separate the [[integer]] part from the [[fractional part]] of a [[number]] written in [[decimal]] form (e.g. "." in 12.45). Different countries officially designate different symbols for use as the separator. The choice of symbol also affects the choice of symbol for the [[thousands separator]] used in digit grouping.
 
[[FIle:Decimal separators.svg|thumb|alt=Four types of separating decimals: a) 1,234.56. b) 1.234,56. c) 1'234,56. d) ١٬٢٣٤٫٥٦.|Both a [[comma]] and a [[full stop]] (or period) are generally accepted decimal separators for international use. The [[apostrophe]] and Arabic decimal separator are also used in certain contexts.]]
Any such symbol can be called a '''decimal mark''', '''decimal marker''', or '''decimal sign'''. Symbol-specific names are also used; '''decimal point''' and '''decimal comma''' refer to an (either [[Baseline dot|baseline]] or [[Middle dot|middle]]) dot and [[comma]] respectively, when it is used as a decimal separator; these are the usual terms used in English,<ref>{{cite web|url=https://www.collinsdictionary.com/dictionary/english/decimal-point|title=Decimal point definition and meaning {{!}} Collins English Dictionary|website=www.collinsdictionary.com|language=en|access-date=2018-07-05}}</ref><ref name=":0">{{Cite web|last=Weisstein|first=Eric W.|title=Decimal Point|url=https://mathworld.wolfram.com/DecimalPoint.html|access-date=2020-08-22|website=mathworld.wolfram.com|language=en}}</ref><ref>{{cite web|url=https://dictionary.cambridge.org/dictionary/english/decimal-point|title=decimal point Meaning in the Cambridge English Dictionary|website=dictionary.cambridge.org|language=en|access-date=2018-07-05}}</ref> with the aforementioned generic terms reserved for abstract usage.<ref>{{Cite news|url=https://www.howtogeek.com/245510/how-to-change-excels-decimal-separators-from-periods-to-commas/|title=How to Change Excel's Decimal Separators from Periods to Commas|access-date=2018-07-05|language=en-US}}</ref><ref>{{Cite news|url=https://www.smartickmethod.com/blog/math/learning-resources/decimal-separators/|title=Decimal Separators: Points or commas? - Elementary Math|date=2018-01-19|work=Elementary Math|access-date=2018-07-05|language=en}}</ref>
[[File:Thousands separators.gif|thumb|Three ways to group the number ten thousand with digit group separators: {{blist
| [[Space (punctuation)|Space]], the internationally recommended thousands separator.
| [[Full stop]] (or period), the thousands separator used in many non-English speaking countries.
| [[Comma]], the thousands separator used in most English-speaking countries.
}}]]
 
A '''decimal separator''' is a symbol usedthat to separateseparates the [[integer]] part from the [[fractional part]] of a [[number]] written in [[decimal]] form (e.g. "." in 12.45). Different countries officially designate different symbols for use as the separator. The choice of symbol also affects the choice of symbol for the [[thousands separator]] used in digit grouping.
In many contexts, when a number is spoken, the function of the separator is assumed by the spoken name of the symbol: ''comma'' or ''point'' in most cases.<ref>{{Cite web|title=Definition of Decimal Point|url=https://www.mathsisfun.com/definitions/decimal-point.html|access-date=2020-08-22|website=www.mathsisfun.com}}</ref><ref name=":0" /><ref>{{Cite news|url=https://www.grammarphobia.com/blog/2012/02/decimal-point.html|title=Mythematics: a decimal point|date=2012-02-17|work=Grammarphobia|access-date=2018-07-05|language=en-US}}</ref> In some specialized contexts, the word ''decimal'' is instead used for this purpose (such as in [[International Civil Aviation Organization]]-regulated [[air traffic control]] communications). In mathematics, the decimal separator is a type of [[Decimal separator#Radix point|radix point]], a term that also applies to number systems with bases other than ten.
 
Any such symbol can be called a '''decimal mark''', '''decimal marker''', or '''decimal sign'''. Symbol-specific names are also used; '''decimal point''' and '''decimal comma''' refer to ana dot (either [[Baseline dot|baseline]] or [[Middle dot|middle]]) dot and [[comma]] respectively, when it is used as a decimal separator; these are the usual terms used in English,<ref>{{cite web|url=https://www.collinsdictionary.com/dictionary/english/decimal-point|title=Decimal point definition and meaning {{!}} Collins English Dictionary|website=www.collinsdictionary.com|language=en|access-date=2018-07-05}}</ref><ref name=":0">{{Cite web|last=Weisstein|first=Eric W.|title=Decimal Point|url=https://mathworld.wolfram.com/DecimalPoint.html|access-date=2020-08-22|website=mathworld.wolfram.com|language=en}}</ref><ref>{{cite web|url=https://dictionary.cambridge.org/dictionary/english/decimal-point|title=decimal point Meaning in the Cambridge English Dictionary|website=dictionary.cambridge.org|language=en|access-date=2018-07-05}}</ref> with the aforementioned generic terms reserved for abstract usage.<ref>{{Cite news|url=https://www.howtogeek.com/245510/how-to-change-excels-decimal-separators-from-periods-to-commas/|title=How to Change Excel's Decimal Separators from Periods to Commas|access-date=2018-07-05|language=en-US}}</ref><ref>{{Cite news|url=https://www.smartickmethod.com/blog/math/learning-resources/decimal-separators/|title=Decimal Separators: Points or commas? - Elementary Math|date=2018-01-19|work=Elementary Math|access-date=2018-07-05|language=en}}</ref>
 
In many contexts, when a number is spoken, the function of the separator is assumed by the spoken name of the symbol: ''comma'' or ''point'' in most cases.<ref>{{Cite web|title=Definition of Decimal Point|url=https://www.mathsisfun.com/definitions/decimal-point.html|access-date=2020-08-22|website=www.mathsisfun.com}}</ref><ref name=":0" /><ref>{{Cite news|url=https://www.grammarphobia.com/blog/2012/02/decimal-point.html|title=Mythematics: a decimal point|date=2012-02-17|work=Grammarphobia|access-date=2018-07-05|language=en-US}}</ref> In some specialized contexts, the word ''decimal'' is instead used for this purpose (such as in [[International Civil Aviation Organization]]-regulated [[air traffic control]] communications). In mathematics, the decimal separator is a type of [[Decimal separator#Radix point|radix point]], a term that also applies to number systems with bases other than ten.
 
==History==
===Hellenistic–Renaissance eras===
{{anchor|Separatrix|Pythagorean arc}}
In the [[Middle Ages]], from the original Indian decimal writing,{{citation needed|date=January 2022}} 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 }}</ref>{{contradict-inline|History of mathematical notation#Indian and Arabic numerals and notation}}
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 |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 ''[[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> 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&nbsp; 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>
Line 35 ⟶ 43:
 
[[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&nbsp;.<ref>{{cite web |author=AndyMax25 cn|date=May 1, 2015 |title=Tenths to fractions |website=AARoads |type=web forum |url=https://www.aaroads.com/forum/index.php?PHPSESSID=48959587c2d49efd64618519aca76fe4&topic=15418.msg2061534#msg2061534 |access-date=July 7,November 20192024}}</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.
 
===ArtificialConstructed languages===
The three most spoken [[international auxiliary language]]s, [[Ido (language)|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, whilewhilst 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 whilewhilst 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, and – somewhat unusually – uses, the middle dot as theits 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 permitspermit 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 ===
Line 63 ⟶ 71:
 
==Current standards==
The 22nd [[General Conference on Weights and Measures]]<ref name=CGPM-22nd-R10/> declared in 2003, that "the“The symbol for the decimal marker shall be either the point on the line or the comma on the line". It further reaffirmed that,
: "numbers“Numbers may be divided in groups of three in order to facilitate reading; neither dots nor commas are ever inserted in the spaces between groups"groups”<ref name=CGPM-22nd-R10>
{{cite conference
|title=Resolution&nbsp;10
Line 74 ⟶ 82:
}}
</ref>
({{nobr|1&thinsp;000&thinsp;000&thinsp;000}} for example).<ref name=CGPM-22nd-R10/> This use has therefore been recommended by technical organizations, such as the United States'States’ [[National Institute of Standards and Technology]].<ref>{{cite report |first1=Ambler |last1=Thompson |first2=Barry N. |last2=Taylor |date=March 2008 |title=Guide for the Use of the International System of Units (SI) |at=§10.5.3 |publisher=[[National Institute of Standards and Technology]] |url=https://physics.nist.gov/cuu/pdf/sp811.pdf#10.5.3 |access-date=21 January 2022}}</ref>
 
Past versions of [[ISO 8601]], but not the 2019 revision, also stipulated normative notation based on SI conventions, adding that the comma is preferred over the full stop.<ref>{{cite report |id=ISO/FDIS 8601:2000(E) |title=Data elements and interchange formats — Information interchange |section=§5.3.1.3 – Representation of dates and times |page=15 |date=2000 |publisher=[[International Standards Organisation]] |url=http://xml.coverpages.org/ISO-FDIS-8601.pdf |access-date=8 January 2019}}</ref>
 
[[ISO 80000-1]] stipulates, that "The“The decimal sign is either a comma or a point on the line." The standard does not stipulate any preference, observing that usage will depend on customary usage in the language concerned, but adds a note that as per ISO/IEC directives, all ISO standards should use the comma as the decimal marker.
 
==Digit grouping==
<!-- Courtesy note per [[WP:RSECT]]: Several redirects link here. (Generally those with "separator" or "thousands" in their titles.) Please check with What Links here before renaming, leaving a hidden [[template:anchor]] to avoid breaking incoming links. See also [[:Talk:Decimal separator#Digit grouping and decimal separating aren't the same]]. -->
 
For ease of reading, numbers with many digits (e.g. numbers over 999) may be divided into groups using a [[delimiter]],<ref name="AMA10p793">{{cite book |last=Iverson |first=Cheryl |display-authors=etal |year=2007 |title=AMA Manual of Style |edition=10th |publisher=[[Oxford University Press]] |location=Oxford, UK |isbn=978-0-19-517633-9 |page=793 |url=https://archive.org/details/amamanualofstyle0000unse/page/793 }}</ref> such as comma "," or dot ".", half-space (or [[thin space]]) {{nobr|"&thinsp;",}} [[Space (punctuation)|space]] {{nobr|"&nbsp;"}}, underscore "_" (as in maritime "21_450") or apostrophe «'»<!-- f.e. in Switzerland -->. In some countries, these "digit group separators" are only employed to the left of the decimal separator; in others, they are also used to separate numbers with a long [[fractional part]]. An important reason for grouping is that it allows rapid judgement of the number of digits, via telling at a glance ("[[subitizing]]") rather than counting (contrast, for example, {{nobr|100&thinsp;000&thinsp;000}} with 100000000 for one hundred million).
 
The use of [[Narrow no-breakThin space|thin spaces]] as separators,<ref name="SIBrochure">{{SIbrochure8th}}</ref>{{rp|page=133}} not dots or commas (for example: {{nobr|20&thinsp;000}} and {{nobr|1&thinsp;000&thinsp;000}} for "twenty thousand" and "one million"), has been official policy of the [[International Bureau of Weights and Measures]] since 1948 (and reaffirmed in 2003) stating
: "neither dots nor commas are ever inserted in the spaces between groups",<ref name=CGPM-22nd-R10/>
 
as well as of the [[International Union of Pure and Applied Chemistry]] (IUPAC),<ref name="BIPM">{{cite report |publisher=[[International Bureau of Weights and Measures]] |title=Rules and style conventions for expressing values of quantities |url=https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-10-more-printing-and-using-symbols-and-numbers}}</ref><ref name="old.iupac.org">{{cite report |title=Guidelines for drafting IUPAC technical reports and recommendations |year=2007 |url=http://old.iupac.org/reports/provisional/guidelines.html |access-date=2008-11-27}}</ref> the [[American Medical Association]]'s widely followed ''[[AMA Manual of Style]]'', and the [[Metrication Board]], among others.
 
The groups created by the delimiters tend to follow the useusages of the local languagelanguages, which varies. In European languages, large numbers are read in groups of thousands, and the delimiter{{Mdash}}which occurs every three digits when it is used{{Mdash}}may be called a "thousands separator". In [[East Asian culture]]s, particularly [[Chinese numerals|China]], [[Japanese numerals|Japan]], and [[Korean numerals|Korea]], large numbers are read in groups of [[myriad]]s (10 &nbsp;000s) but the delimiter commonly separates every three digits.{{citation needed|date=February 2014}}<!-- see talk page -->
 
The [[Indian numbering system]] is somewhat more complex: It groups the rightmost three digits together (until the hundreds place) and thereafter groups by sets of two digits. For example, one [[Short trillion|American trillion]] (European [[billion]]) would thus be written as 10,00,00,00,00,000 or 10 [[Indian numbering system|kharab]].<ref>{{cite report |last=Emmons |first=John |date=2018-03-25 |section=Part&nbsp;3: Numbers |title=Unicode Locale Data Markup Language (LDML) |website=Unicode.org |section-url=https://www.unicode.org/reports/tr35/tr35-numbers.html#Special_Pattern_Characters |url-status=live |access-date=2018-03-25 |archive-url=https://web.archive.org/web/20180725183458/https://www.unicode.org/reports/tr35/tr35-numbers.html#Special_Pattern_Characters |archive-date=2018-07-25}}</ref>
Line 96 ⟶ 104:
The convention for digit group separators historically varied among countries, but usually seeking to distinguish the delimiter from the decimal separator. Traditionally, [[English-speaking countries]] (except South Africa)<ref>{{Cite web |url=https://extranet.education.unimelb.edu.au/SME/TNMY/Decimals/Decimals/backinfo/overseas.htm |title=Language and Culture Differences. |website=extranet.education.unimelb.edu.au |accessdate=11 March 2023}}</ref> employed commas as the delimiter – 10,000 – and other European countries employed periods or spaces: 10.000 or {{nobr|10&thinsp;000}}. Because of the confusion that could result in international documents, in recent years the use of spaces as separators has been advocated by the superseded [[ISO 31-0#Numbers|SI/ISO 31-0 standard]],<ref name="nist.gov">{{cite web |title=Decimals Score a Point on International Standards |date=2006-11-22 |publisher=U.S. [[National Institute of Standards and Technology]] |url=https://www.nist.gov/public_affairs/techbeat/tb2006_1122.htm#decimal |url-status=dead |access-date=2008-11-27 |archive-url=https://web.archive.org/web/20160303171543/https://www.nist.gov/public_affairs/techbeat/tb2006_1122.htm#decimal |archive-date=2016-03-03 }}</ref> as well as by the [[International Bureau of Weights and Measures]] and the [[International Union of Pure and Applied Chemistry]], which have also begun advocating the use of a "[[thin space]]" in "groups of three".<ref name="BIPM"/><ref name="old.iupac.org"/>
 
Within the United States, the [[American Medical Association]]'s widely followed ''[[AMA Manual of Style]]'' also calls for a thin space.<ref name="AMA10p793"/> In someprogramming languages and online [[character encoding|encoding]] environments (for example, [[ASCII]]-only) a thin space is not practical or available, in which case aan underscore,<ref>{{cite web|url=https://peps.python.org/pep-0515/#prior-art|title=PEP 515 Underscores in Numeric Literals: Prior Art|website=peps.python.org|accessdate=2024-02-13}}</ref> regular word space, or no delimiter are the alternatives.
 
===Data versusvis-à-vis mask===
Digit group separators can occur either as part of the data or as a mask through which the data is displayed. This is an example of the [[separation of presentation and content]], making it possible to display numbers with spaced digit grouping in a way that does not insert any [[whitespace character]]s into the string of digits in the [[digital content|content]]. In many computing contexts, it is preferred to omit digit group separators from the data and instead overlay them as a mask (an [[input mask]] or an output mask).
 
Line 114 ⟶ 122:
: [[Haskell (programming language)|Haskell]] {{nobr|&emsp; {{small|(from GHC version 8.6.1)}} }}
: [[Java (programming language)|Java]]
: [[JavaScript]]
: [[Kotlin (programming language)|Kotlin]]<ref>{{cite web |title=Basic types |website=Kotlin Language |url=https://kotlinlang.org/docs/basic-types.html#literal-constants:~:text=You%20can%20use%20underscores%20to%20make%20number%20constants%20more%20readable}}</ref>
: [[OCaml]]
Line 121 ⟶ 130:
: [[Ruby (programming language)|Ruby]]
: [[Rust (programming language)|Rust]]
: [[Zig (programming language)|Zig]]
{{div col end}}
 
[[Julia (programming language)|Julia]], [[Swift (programming language)|Swift]], [[Java (programming language)|Java]], and free-form [[Fortran 90]] use the [[Underscore|underscore (_)]] character for this purpose; as such, these languages allow seven hundred million to be entered as 700_000_000.
 
Fixed-form [[Fortran]] ignores [[whitespace character|whitespace]] (in all contexts), so 700&nbsp;000&nbsp;000 has always been accepted. [[Fortran 90]] and its successors allow (ignored) underscores in numbers in free-form.
Line 152 ⟶ 162:
In countries with a decimal comma, the decimal point is also common as the "international" notation{{citation needed|date=May 2022}} because of the influence of devices, such as [[electronic calculator]]s, which use the decimal point. Most computer [[operating systems]] allow selection of the decimal separator; programs that have been carefully [[i18n|internationalized]] will follow this, but some programs ignore it and a few may even fail to operate if the setting has been changed.
 
Computer interfaces may be set to the Unicode international "Common locale" using {{code| LC_NUMERIC{{=}}C }} as defined at {{cite web |title=Unicode CLDR project |website=[[Unicode Consortium]] |url=http://cldr.unicode.org/index}} Details of the current (2020) definitions may be found at {{cite web |title=01102-POSIX15897 |website=[[Unicode Consortium]] |url=http://www.unicode.org/L2/L2001/01102-POSIX15897.htm}}
[[File:DecimalSeparator.svg|300px|thumb|Decimal separators:
 
==Conventions worldwide==
[[File:DecimalSeparator.svg|300px600px|thumb|center|Decimal separators:
{{legend|#00b7ef|Dot (.)}}
{{legend|#a8e61d|Comma (,)}}
{{legend|#54ce86|Both (may vary by location or other factors)}}
{{legend|#ed1c24|[[#Other numeral systems|Arabic decimal separator]] ({{Script|Arab|٫}})}}
{{legend|#c0c0c0|Data unavailable}}]]
 
{{Cleanup|Conventionssection worldwide,and Examplesthe ofsection usethat follows it|reason=Use by region is inconsistent, inaccurate, and are poorly formatted.|date=March 2023}}
Computer interfaces may be set to the Unicode international "Common locale" using {{code| LC_NUMERIC{{=}}C }} as defined at {{cite web |title=Unicode CLDR project |website=[[Unicode Consortium]] |url=http://cldr.unicode.org/index}} Details of the current (2020) definitions may be found at {{cite web |title=01102-POSIX15897 |website=[[Unicode Consortium]] |url=http://www.unicode.org/L2/L2001/01102-POSIX15897.htm}}
 
==Conventions worldwide==
{{More citations needed|section|date=August 2023}}
 
Line 211 ⟶ 222:
* Kazakhstan
* Kyrgyzstan
* Laos
* Latvia
* Lebanon
* Lithuania
* Luxembourg
* Luxembourg (uses both marks officially{{Citation needed|date=December 2022}})
* Macau (in Portuguese text)
* Mauritania
Line 232 ⟶ 244:
* Romania
* Russia
* San Marino
* Serbia
* Slovakia
Line 287 ⟶ 300:
* Libya
* Liechtenstein
* Luxembourg (uses both marks officially){{Citation needed|date=December 2022}}
* Macau (in Chinese and English text)
* Malaysia
Line 317 ⟶ 329:
* United Kingdom
* United States (including [[insular area]]s)
}}Notes:{{notelist|group=lower-roman}}
}}
{{notelist|group=lower-roman}}
 
===Other numeral systems===
Line 325 ⟶ 336:
In the [[Arab world]], where [[Eastern Arabic numerals]] are used for writing numbers, a different character is used to separate the integer and fractional parts of numbers. It is referred to as an [[Arabic (Unicode block)|Arabic decimal separator]] (U+066B, rendered: {{Script|Arab|٫}}) in [[Unicode]]. An Arabic thousands separator (U+066C, rendered: {{Script|Arab|٬}}) also exists. Example: {{Script|Arab|۹٬۹۹۹٫۹۹}} (9,999.99)
 
In [[Persian language|Persian]], the decimal separator is called [[#Other_numeral_systems|momayyez]]. The Unicode Consortium's investigation concluded that "computer programs should render U+066B as a shortened, lowered, and possibly more slanted [[Slash (punctuation)|slash]] ({{Script|fa-Arab|٫}}); this should be distinguishable from the slash at the first sight." To separate [[sequence]]s of three digits, an Arabic thousands separator (rendered as: {{Script|fa-Arab|٬}}), a Latin comma, or a [[space (punctuation)|blank space]] may be used; however this is not a standard.<ref>{{cite web |url=http://unicode.org/mail-arch/unicode-ml/Archives-Old/UML024/1289.html |title=Persian decimal separator |last=Pournader |first=Roozbeh |date=2000-10-15 |work=Unicode Mail List Archive |publisher=Unicode Consortium |access-date=2008-06-21}}</ref><ref>{{cite web
|url=http://www.fazel.de/dastur/EN/2-1-05-001-1-3_decimal_numeral.html
|title=The Decimal Numeral
Line 344 ⟶ 355:
! Style !! Countries and regions
|-
| style="text-align:right;"| 1'''<nowiki>,</nowiki>'''234'''<nowiki>,</nowiki>'''567'''<nowiki>.</nowiki>'''89 || Australia,<ref>{{cite web|url=https://www.stylemanual.gov.au/style-rules-and-conventions/numbers-and-measurements/choosing-numerals-or-words#combine_numerals_and_words_for_large_rounded_numbers|title=Digital Guides|publisher=Australian Government|access-date=19 August 2020}}</ref><ref>{{cite web|url=https://about.abc.net.au/abc-editorial/the-abc-style-guide/#T|title=The ABC Style Guide|publisher=Australian Broadcasting Corporation|access-date=19 August 2020}}</ref> Cambodia, Canada (English-speaking; unofficial), China,<ref name="SAMR2011">{{cite web|url=https://openstd.samr.gov.cn/bzgk/gb/newGbInfo?hcno=F5DAC3377DA99C8D78AE66735B6359C7|title=国家标准GB/T 15835-2011出版物上数字用法|publisher=国家标准全文公开系统|access-date=2 April 2024|date=2011-07-29|language=zh|trans-title=General rules for writing numerals in public texts}}</ref> Cyprus (currency numbers), Hong Kong, Iran, Ireland, Israel, Japan, Korea, Macau (in Chinese and English text), Malaysia, Malta, Mexico, Namibia, New Zealand, Pakistan, Peru (currency numbers), Philippines, Singapore, South Africa (English-speaking; unofficial), Taiwan, Thailand, United Kingdom and other Commonwealth states except Mozambique, United States.
|-
| style="text-align:right;"| {{gaps|1|234|567'''<nowiki>.</nowiki>'''89}} || SI style (English version), Canada (English-speaking; official), China,<ref name="SAMR2011" /> Estonia (currency numbers), Hong Kong (in education), Mexico, Namibia, South Africa (English-speaking; unofficial), Sri Lanka, Switzerland (in federal texts for currency numbers only<ref name="bk_admin_ch">{{cite web |publisher=Schweizer Bundeskanzlei |url=https://www.admin.ch/gov/de/start/dokumentation/medienmitteilungen.msg-id-49648.html |title=Schreibweisungen, 2nd edition 2013 |date=June 2013 |archive-url=https://web.archive.org/web/20150128123857/http://www.bk.admin.ch/dokumentation/sprachen/04915/05016/index.html?lang=de&download=NHzLpZeg7t,lnp6I0NTU042l2Z6ln1acy4Zn4Z2qZpnO2Yuq2Z6gpJCHe393gWym162epYbg2c_JjKbNoKSn6A-- |archive-date= 28 January 2015}}</ref>), United Kingdom (in education), United States (in education){{Citation needed|date=September 2024|reason=Based on my experience, the overwhelming majority of academia in the US uses the thousand separator.}}. SI style (English version) but SI doesn't include currency.
|-
| style="text-align:right;"| {{gaps|1|234|567'''<nowiki>,</nowiki>'''89}} || SI style (French version), Albania, Belgium (French), Brazil, Bulgaria, Canada (French-speaking), Costa Rica, Croatia, Czech Republic, Estonia, Finland,<ref>{{cite web|url=http://www.kielitoimistonohjepankki.fi/ohje/49|title=Luvut ja numerot: numeroiden ryhmittely|website=Kielitoimiston ohjepankki|language=fi-FI|access-date=2018-06-27}}</ref> France, Hungary, Italy (in education), Latin America, Latin Europe, Latvia, Lithuania, Macau (in Portuguese text), Mozambique, Norway, Peru, Poland, Portugal, Russia, Serbia (informal), Slovakia, Slovenia, South Africa (official<ref name=SAHPRA>{{cite report |url=https://www.sahpra.org.za/wp-content/uploads/2020/01/2.38_SI_Metric_System_Mar19_v3.pdf |title=SI Metric System |date=March 2019 |edition=2.38 |website=SAHPRA |quote=The comma is the only recognised decimal indicator for all numbers, including amounts of (currency) money.}}</ref>), Spain (official use since 2010, according to the ''[[Royal Spanish Academy|RAE]]'' and ''[[Spanish National Research Council|CSIC]]''), Sweden, Switzerland (in federal texts, except currency numbers<ref name=bk_admin_ch/>), Ukraine, Vietnam (in education). SI style (French version) but SI doesn't include currency.
|-
| style="text-align:right;"| 1'''<nowiki>.</nowiki>'''234'''<nowiki>.</nowiki>'''567'''<nowiki>,</nowiki>'''89 || Austria, Belgium (Dutch), Bosnia and Herzegovina, Brazil (informal and in [[technology]]), Chile, Colombia, Croatia (in [[bookkeeping]] and technology),<ref name=":1">{{Cite web |title=Točka |website=Hrvatski pravopis |publisher=[[Institute of Croatian Language and Linguistics]] |url=http://pravopis.hr/pravilo/tocka/55/ |access-date=2022-07-28}}</ref> Denmark, Germany, Greece, Indonesia, Italy, Latin America (informal), Netherlands, Romania, Slovenia, Serbia, Spain (used until 2010, inadvisable use according to the ''[[Royal Spanish Academy|RAE]]'' and [[Spanish National Research Council|''CSIC'']]),{{efn|... when writing numbers more than four figures, these will be grouped into threes, starting from the right, and separating the groups by whitespace. (Exceptions: Never written with periods, commas or white separation numbers that refer to years, pages, verses, urban roads, postal codes, legal articles, decrees or laws.)<ref name=test>{{cite book |title=Diccionario panhispánico de dudas |url=http://lema.rae.es/dpd/srv/search?key=n%FAmeros#2 |url-status=dead |access-date=16 January 2014 |archive-date=18 January 2014 |archive-url=https://web.archive.org/web/20140118023207/http://lema.rae.es/dpd/srv/search?key=n%FAmeros#2 }}</ref>}}<ref name=Ortografia>{{cite book |title=Ortografía de la lengua española |quote=For the purpose of promoting a process tending towards unification, the use of the point as decimal separator is recommended.(2.2.1.2.1) |url=http://aplica.rae.es/orweb/cgi-bin/v.cgi?i=KnJfwDWVQQYgmiw,}}</ref> Turkey, Uruguay, Vietnam.
|-
| style="text-align:right;"| 1'''<nowiki>,</nowiki>'''234'''<nowiki>,</nowiki>'''567'''<nowiki>·</nowiki>'''89 || Malaysia, Malta, Philippines (uncommon today), Singapore, Taiwan, United Kingdom (older, typically handwritten; in education)
|-
| style="text-align:right;"| 12'''<nowiki>,</nowiki>'''34'''<nowiki>,</nowiki>'''567'''<nowiki>.</nowiki>'''89 || rowspan="2" | Bangladesh, India, Nepal, Pakistan (see [[Indian numbering system]]).
|-
|{{Gaps|12|34|567'''<nowiki>.</nowiki>'''89}}
|Bangladesh, India, Nepal, Pakistan (see [[Indian numbering system]]).
|-
| style="text-align:right;"| 1'''<nowiki>'</nowiki>'''234'''<nowiki>'</nowiki>'''567'''<nowiki>.</nowiki>'''89 || Switzerland (computing), Liechtenstein.
Line 363 ⟶ 373:
| style="text-align:right;"| 1'''<nowiki>'</nowiki>'''234'''<nowiki>'</nowiki>'''567'''<nowiki>,</nowiki>'''89 || Switzerland (handwriting), Italy (handwriting).
|-
| style="text-align:right;"| 1'''<nowiki>.</nowiki>'''234'''<nowiki>.</nowiki>'''567'''<nowiki>'</nowiki>'''89 || Spain (handwriting, used until 1980s, inadvisable use according to the [[Royal Spanish Academy|''RAE'']] and ''[[Spanish National Research Council|CSIC]]''{{Citation needed|date=October 2009}}).
|-
| style="text-align:right;"| 123'''<nowiki>,</nowiki>'''4567'''<nowiki>.</nowiki>'''89 || Mainland China (based on powers of 10 000—see [[Chinese numerals]]{{Citation needed|date=April 2019}}).
|-
|{{Gaps|123|4567'''<nowiki>.</nowiki>'''89}}
|Mainland China (based on powers of 10 000—see [[Chinese numerals]]{{Citation needed|date=April 2019}}).
|}
 
*In Albania, Belgium (French), Estonia, Finland,<ref>{{cite web|url=http://www.kielitoimistonohjepankki.fi/ohje/49|title=Luvut ja numerot: numeroiden ryhmittely|website=Kielitoimiston ohjepankki|language=fi-FI|access-date=2018-06-27}}</ref> France, Hungary, Poland, Slovakia and much of [[Romance-speaking Europe|Latin Europe]] as well as French Canada: {{gaps|1|234|567'''<nowiki>,</nowiki>'''89}} (In Spain, in handwriting it is also common to use an upper comma: 1'''<nowiki>.</nowiki>'''234'''<nowiki>.</nowiki>'''567'''<nowiki>'</nowiki>'''89){{Citation needed|date=October 2009}}
*In Belgium (Dutch), Brazil, Denmark, Germany, Greece, Indonesia, Italy, Netherlands, Portugal, Romania, Russia, Slovenia, Sweden and much of Europe: {{gaps|1|234|567'''<nowiki>,</nowiki>'''89}} or 1'''<nowiki>.</nowiki>'''234'''<nowiki>.</nowiki>'''567'''<nowiki>,</nowiki>'''89. In [[handwriting]], 1'''<nowiki>˙</nowiki>'''234'''<nowiki>˙</nowiki>'''567'''<nowiki>,</nowiki>'''89 is also seen, but never in Belgium, Brazil, Denmark, Estonia, Germany, the Netherlands, Portugal, Romania, Russia, Slovenia or Sweden. In Italy, a straight apostrophe is also used in handwriting: 1'''<nowiki>'</nowiki>'''234'''<nowiki>'</nowiki>'''567'''<nowiki>,</nowiki>'''89. In the Netherlands and Dutch-speaking Belgium, the points thousands separator is used, and is preferred for currency amounts, but the space is recommended by some style guides, mostly in technical writing.<ref>{{cite web|url=http://taaladvies.net/taal/advies/vraag/1/10000000_10_000_000/|title=10.000.000&nbsp;/&nbsp;10&nbsp;000&nbsp;000|author=Taalunieversum|access-date=1 September 2017}}</ref>
*In Estonia, currency numbers often use a dot "'''<nowiki>.</nowiki>'''" as the decimal separator, and a space as a thousands separator. This is most visible on shopping receipts and in documents that also use other numbers with decimals, such as measurements. This practice is used to better distinguish between prices and other values with decimals. An older convention uses dots to separate thousands (with commas for decimals) &mdash; this older practice makes it easier to avoid word breaks with larger numbers.
Line 385 ⟶ 389:
{|class="wikitable" style="text-align:center;"
|-
!Indian Valuevalue
!Value
!Equivalent Westernwestern Notationnotation
|-
|scope="row" |One
Line 407 ⟶ 411:
|scope="row" |Lakh
| style="text-align:right;"|1'''<nowiki>,</nowiki>'''00'''<nowiki>,</nowiki>'''000
|One Hundredhundred Thousandthousand
|-
|scope="row" |Crore
| style="text-align:right;"|1'''<nowiki>,</nowiki>'''00'''<nowiki>,</nowiki>'''00'''<nowiki>,</nowiki>'''000
|Ten Millionmillion
|-
|scope="row" | Arab (not normally used)
| style="text-align:right;"|1'''<nowiki>,</nowiki>'''00'''<nowiki>,</nowiki>'''00'''<nowiki>,</nowiki>'''00'''<nowiki>,</nowiki>'''000
|One [[ShortLong Billion|Shortand (American)short Billionscales|short]] billion (Oneone Thousandthousand Millionmillion)
|-
|scope="row" | Kharab (not normally used)
| style="text-align:right;"|1'''<nowiki>,</nowiki>'''00'''<nowiki>,</nowiki>'''00'''<nowiki>,</nowiki>'''00'''<nowiki>,</nowiki>'''00'''<nowiki>,</nowiki>'''000
|One Hundredhundred Shortshort Billionbillion
|-
|scope="row" | Lakh Crorecrore
| style="text-align:right;"|10'''<nowiki>,</nowiki>'''00'''<nowiki>,</nowiki>'''00'''<nowiki>,</nowiki>'''00'''<nowiki>,</nowiki>'''00'''<nowiki>,</nowiki>'''000
|One [[Shortshort Trillion]]trillion (Oneone Longlong (European) Billionbillion)
|}
{{Clear|Left}}
Line 453 ⟶ 457:
* [[Decimal place]]
* [[Decimal representation]]
* ''[[Scriptio continua]]''
* [[Space (punctuation)]]
* [[Decimal section numbering]]
* [[Dot-decimal notation]]