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Adecimal separator is a symbol that separates theinteger part from thefractional part of anumber written indecimal form. Different countries officially designate different symbols for use as the separator. The choice of symbol can also affect the choice of symbol for thethousands separator used in digit grouping.
Any such symbol can be called adecimal mark,decimal marker, ordecimal sign. Symbol-specific names are also used;decimal point anddecimal comma refer to a dot (eitherbaseline ormiddle) andcomma respectively, when it is used as a decimal separator; these are the usual terms used in English,[1][2][3] with the aforementioned generic terms reserved for abstract usage.[4][5]
In many contexts, when a number is spoken, the function of the separator is assumed by the spoken name of the symbol:comma orpoint in most cases.[6][2][7] In some specialized contexts, the worddecimal is instead used for this purpose (such as inInternational Civil Aviation Organization-regulatedair traffic control communications). In mathematics, the decimal separator is a type ofradix point, a term that also applies to number systems with bases other than ten.
In theMiddle Ages, before printing, abar ( ¯ ) over theunits digit was used to separate the integral part of a number from itsfractional part, as in 9995 (meaning 99.95 indecimal 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 9995. Later, a "separatrix" (i.e., a short, roughly vertical ink stroke) between the units and tenths position became the norm amongArab mathematicians (e.g. 99ˌ95), while an L-shaped orvertical bar (|) served as the separatrix in England.[8] When this character wastypeset, it was convenient to use the existingcomma (99,95) orfull stop (99.95) instead.
Positionaldecimal fractions appear for the first time in a book by the Arab mathematicianAbu'l-Hasan al-Uqlidisi written in the 10th century.[9] The practice is ultimately derived from the decimalHindu–Arabic numeral system used inIndian mathematics,[10] and popularized by thePersian mathematicianAl-Khwarizmi,[11] whenLatin translation ofhis work on theIndian numerals introduced the decimalpositional number system to the Western world. HisCompendious Book on Calculation by Completion and Balancing presented the first systematic solution oflinear andquadratic equations in Arabic.
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 century.Fibonacci followed this convention when writing numbers, such as in his influential workLiber Abaci in the 13th century.[12]
The earliest known record of using the decimal point is in the astronomical tables compiled by the Italian merchant and mathematicianGiovanni Bianchini in the 1440s.[13][contradictory]
Tables oflogarithms prepared byJohn Napier in 1614 and 1619 used the period (full stop) as the decimal separator, which was then adopted byHenry Briggs in his influential 17th century work.
InFrance, the full stop was already in use in printing to makeRoman numerals more readable, so the comma was chosen.[14]
Many other countries, such as Italy, also chose to use the comma to mark the decimal units position.[14] It has beenmade standard by theISO for international blueprints.[15] However, English-speaking countries took the comma to separate sequences of three digits. In some countries, a raised dot or dash (upper comma) may be used for grouping or decimal separator; this is particularly common in handwriting.
In theUnited States, the full stop or period (.) is used as the standard decimal separator.
In the nations of theBritish Empire (and, later, theCommonwealth of Nations), the full stop could be used in typewritten material and its use was not banned, although theinterpunct (a.k.a. decimal point, point or mid dot) was preferred as a decimal separator, in printing technologies that could accommodate it, e.g. 99·95 .[17] However, as the mid dot was already in common use in the mathematics world to indicate multiplication, theSI rejected its use as the decimal separator.
During the beginning of Britishmetrication in the late 1960s and with impending currencydecimalisation, there was some debate in the United Kingdom as to whether the decimal comma or decimal point should be preferred: theBritish Standards Institution and some sectors of industry advocated the comma and theDecimal Currency Board advocated for the point. In the event, the point was chosen by theMinistry of Technology in 1968.[18]
When South Africaadopted the metric system, it adopted the comma as its decimal separator,[19] although a number of house styles, including some English-language newspapers such asThe Sunday Times, continue to use the full stop.[citation needed]
Previously, signs alongCalifornia roads expressed distances in decimal numbers with the decimal part in superscript, as in 37, meaning 3.7.[20] Though California has since transitioned tomixed numbers withcommon fractions, the older style remains onpostmile markers and bridge inventory markers.
The three most spokeninternational auxiliary languages,Ido,Esperanto, andInterlingua, all use the comma as the decimal separator.
Interlingua has used the comma as its decimal separator since the publication of theInterlingua Grammar in 1951.[21]
Esperanto also uses the comma as its official decimal separator, whilst thousands are usually separated bynon-breaking spaces (e.g.12 345 678,9). It is possible to separate thousands by afull stop (e.g.12.345.678,9), though this is not as common.[22]
Ido'sKompleta 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 written12.345.678,90123 in Ido.
The 1931 grammar ofVolapük uses the comma as its decimal separator but, somewhat unusually, the middle dot as its thousands separator (12·345·678,90123).[23]
In 1958, disputes between European and American delegates over the correct representation of the decimal separator nearly stalled the development of theALGOL computer programming language.[24] ALGOL ended up allowing different decimal separators, but most computer languages and standard data formats (e.g.,C,Java,Fortran,Cascading Style Sheets (CSS)) specify a dot.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).
In mathematics andcomputing, aradix point orradix character is a symbol used in the display of numbers to separate theinteger part of the value from itsfractional 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.[25]
A radix point is most often used indecimal (base 10) notation, when it is more commonly called thedecimal point (withdeci- indicatingbase 10). InEnglish-speaking countries, the decimal point is usually a small dot (.) placed either on the baseline, or halfway between the baseline and the top of thedigits (·)[26][a]In many other countries, the radix point is a comma (,) placed on the baseline.[26][a]
These conventions are generally used both in machine displays (printing,computer monitors) and inhandwriting. It is important to know which notation is being used when working in different software programs. The respectiveISO 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 othernumber bases, but, when they are, a radix character may be used for the same purpose. When used with thebinary (base 2) representation, it may be called "binary point".
The 22ndGeneral Conference on Weights and Measures[27] declared in 2003, "The symbol for the decimal marker shall be either the point on the line or the comma on the line." It further reaffirmed,[27]
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
That is, "1 000 000 000" is preferred over "1,000,000,000" or "1.000.000.000". This use has therefore been recommended by technical organizations, such as the United States'sNational Institute of Standards and Technology.[28]
Past versions ofISO 8601, but not the 2019 revision, also stipulated normative notation based on SI conventions, adding that the comma is preferred over the full stop.[29]
ISO 80000-1 stipulates, "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.
For ease of reading, numbers with many digits (e.g. numbers over 999) may be divided into groups using adelimiter,[30] such as comma (,), dot (.), half-space orthin space (" "),space (" "), underscore (_; as in maritime "21_450"),[citation needed] or apostrophe ('). 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 longfractional 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,100 000 000 with 100000000 for one hundred million).
The use of thin spaces as separators[31]: 133 instead of dots or commas (for example:20 000 and1 000 000 for "twenty thousand" and "one million"), has been official policy of theInternational Bureau of Weights and Measures (BIPM) since 1948 (and reaffirmed in 2003),[27]as well as of theInternational Union of Pure and Applied Chemistry (IUPAC),[32][33] theAmerican Medical Association's widely followedAMA Manual of Style, and the UKMetrication Board, among others.
The groups created by the delimiters tend to follow the usages of local languages, which vary. In European languages, large numbers are read in groups of thousands, and the delimiter (occurring every three digits when used) may be called a "thousands separator". InEast Asian cultures, particularlyChina,Japan, andKorea, large numbers are read in groups ofmyriads (10 000s), but the delimiter often separates the digits into groups of three.[citation needed]
TheIndian numbering system is more complex: It groups the rightmost three digits together (until the hundreds place) and then groups digits in sets of two. For example, one trillion would be written "10,00,00,00,00,000" or "10kharab".[34]
The convention for digit group separators historically varied among countries, but usually sought to distinguish the delimiter from the decimal separator. Traditionally,English-speaking countries (except South Africa)[35] employed commas as the delimiter – 10,000 – and other European countries employed periods (full stops) or spaces: 10.000 or10 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 supersededSI/ISO 31-0 standard,[36] as well as by the BIPM and IUPAC. These groups have also begun advocating the use of a "thin space" in "groups of three".[32][33]
Within the United States, the American Medical Association's widely followedAMA Manual of Style also calls for a thin space.[30] In programming languages and onlineencoding environments (for example,ASCII-only languages and environments) a thin space is not practical or available. Often, either underscores[37] and regular word spaces, or no delimiters at all are used instead.
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 theseparation of presentation and content, making it possible to display numbers in spaced groups while not inserting anywhitespace characters into the string of digits that make up those numbers. In many computing contexts, it is preferred to omit the digit group separators from the data and instead overlay them as a mask (aninput mask or an output mask).
Common examples includespreadsheets anddatabases, in which currency values are entered without such marks but are displayed with them inserted. Similarly, phone numbers can have hyphens, spaces or parentheses as a mask rather than as data. Inweb content, digit grouping can be done withCSS. This is useful because the number can be copied and pasted elsewhere (such as into a calculator) and parsed by the computer as-is (i.e., without the user manually purging the extraneous characters). For example:
In someprogramming languages, it is possible to group the digits in the program'ssource code to make it easier to read(see:Integer literal § Digit separators). Examples include:Ada,C# (sinceversion 7.0),[38]D,Go (sinceversion 1.13),Haskell (from GHCversion 8.6.1),Java,JavaScript (sinceES2021),Kotlin,[39]OCaml,Perl,Python (sinceversion 3.6),PHP (sinceversion 7.4),[40]Ruby,Rust andZig.
Java, JavaScript,Swift,Julia and free-formFortran 90 use theunderscore (_) character for this purpose. As such, these languages would allow the number seven hundred million to be entered as "700_000_000". On the other hand, fixed-form Fortran ignores whitespace in all contexts, so "700 000 000" would be allowed. InC++14,Rebol andRed, the use of anapostrophe for digit grouping is allowed. Thus, "700'000'000" would be allowed in those languages.
The code shown below, written in Kotlin, illustrates the use of separators to increase readability:
valexampleNumber=12_000_000// twelve million
The International Bureau of Weights and Measures states that "when there are only four digits before or after the decimal marker, it is customary not to use a space to isolate a single digit."[32] Likewise, somemanuals of style state that thousands separators should not be used in normal text for numbers from1000 to9999 where no decimal fractional part is shown (or, in other words, for four-digit whole numbers), whereas others use thousands separators and others use both. For example,APA style stipulates a thousands separator for "most figures of1000 or more" except for page numbers, binary digits, temperatures, etc.
There are always "common-sense" country-specific exceptions to digit grouping, such as year numbers,postal codes, and ID numbers of predefined nongrouped format, which style guides usually point out.
In binary (base-2), a full space can be used between groups of four digits, corresponding to anibble, or equivalently to ahexadecimal digit. For integer numbers, dots are used as well to separate groups of four bits.[b]Alternatively, binary digits may be grouped by threes, corresponding to anoctal digit. Similarly, in hexadecimal (base-16), full spaces are usually used to group digits into twos, making each group correspond to abyte.[c] Additionally, groups of eight bytes are often separated by a hyphen.[c]
In countries with a decimal comma, the decimal point is also common as the "international" notation[citation needed] because of the influence of devices, such aselectronic calculators, which use the decimal point. Most computeroperating systems allow selection of the decimal separator; programs that have been carefullyinternationalized 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" usingLC_NUMERIC=C as defined at"Unicode CLDR project".Unicode Consortium. Details of the current (2020) definitions may be found at"01102-POSIX15897".Unicode Consortium.
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Countries where a comma (,) is used as a decimal separator include:
Countries where a dot (.) is used as a decimal separator include:
Notes
Unicode defines adecimal separator key symbol (⎖ in hex U+2396, decimal 9110) which looks similar to theapostrophe. This symbol is fromISO/IEC 9995 and is intended for use on a keyboard to indicate a key that performs decimal separation.
In theArab world, whereEastern 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 anArabic decimal separator (U+066B, rendered:٫) inUnicode. An Arabic thousands separator (U+066C, rendered:٬) also exists. Example:۹٬۹۹۹٫۹۹ (9,999.99)
InPersian, the decimal separator is calledmomayyez. The Unicode Consortium's investigation concluded that "computer programs should render U+066B as a shortened, lowered, and possibly more slantedslash (٫); this should be distinguishable from the slash at the first sight." To separatesequences of three digits, an Arabic thousands separator (rendered as:٬), a Latin comma, or ablank space may be used; however this is not a standard.[49][50][51] Example:۹٬۹۹۹٫۹۹ (9,999.99)
InEnglish Braille, the decimal point,⠨, is distinct from both the comma,⠂, and the full stop,⠲.
The following examples show the decimal separator and the thousands separator in various countries that use the Arabic numeral system.
| Style | Countries and regions |
|---|---|
| 1,234,567.89 | Australia,[52][53] Cambodia, Canada (English-speaking; unofficial), China,[54] Cyprus (currency numbers), Hong Kong, Iran, Ireland, Israel, Japan, Korea, Macau (in Chinese and English text), Malaysia, 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. |
| 1234567.89 | Canada (English-speaking; official), China,[54] Estonia (currency numbers), Hong Kong (in education), Mexico, Namibia, South Africa (English-speaking; unofficial), Sri Lanka, Switzerland (in federal texts for currency numbers only[55]), United Kingdom (in education), United States (in education).[citation needed] SI-style (English version), not including currency. |
| 1234567,89 | Albania, Belgium (French), Brazil, Bulgaria, Canada (French-speaking), Costa Rica, Croatia, Czech Republic, Estonia, Finland,[56] France, Germany, 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[57]), Spain (official use since 2010, according to theRAE andCSIC), Sweden, Switzerland (in federal texts, except currency numbers[55]), Ukraine, Vietnam (in education). SI-style (French version), not including currency. |
| 1.234.567,89 | Austria, Belgium (Dutch), Bosnia and Herzegovina, Brazil (informal and intechnology), Chile, Colombia, Croatia (inbookkeeping and technology),[58] Denmark, Germany, Greece, Indonesia, Italy, Latin America (informal), Netherlands, Romania, Slovenia, Serbia, Spain (used until 2010, inadvisable use according to theRAE andCSIC),[d][60] Turkey, Uruguay, Vietnam. |
| 1,234,567·89 | Malaysia, Malta, Philippines (uncommon today), Singapore, Taiwan, United Kingdom (older, typically handwritten; in education) |
| 12,34,567.89 | Bangladesh, India, Nepal, Pakistan(see:Indian numbering system). |
| 1234567.89 | |
| 1'234'567.89 | Switzerland (computing), Liechtenstein. |
| 1'234'567,89 | Switzerland (handwriting), Italy (handwriting). |
| 1.234.567'89 | Spain (handwriting, used until 1980s, inadvisable use according to theRAE andCSIC[citation needed]). |
') is also used in handwriting: "1'234'567,89". In the Netherlands and Dutch-speaking Belgium, points are used as thousands separators, and is preferred for currency values, but the space is recommended by some style guides, mostly in technical writing.[61].) 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) – this older practice makes it easier to avoid word breaks with larger numbers.') as a thousands separator along with a dot (.) as the decimal separator, like "1'234'567.89". For other values, the SI-style "1234567,89" is used, with a comma (,) as the decimal separator. The apostrophe is also the most common thousands separator for non-currency values, like "1'234'567,89"..) is used in the English version, while a comma (,) is used in the official French version.:) is sometimes used as the decimal separator for currency values, like "1 234 567:89".,) are used at the thousands,lakh, andcrore levels. For example,10 million (1crore) would be written "1,00,00,000", while100 thousand (1lakh) would be written "1,00,000". InPakistan, there is a greater tendency to use the standard western system, but the Indian numbering system is used when conducting business inUrdu.| Indian value | Value | Equivalent western notation |
|---|---|---|
| One | 1 | One |
| Ten | 10 | Ten |
| Hundred | 100 | Hundred |
| Thousand | 1,000 | Thousand |
| Lakh | 1,00,000 | One hundred thousand |
| Crore | 1,00,00,000 | Ten million |
| Arab (not normally used) | 1,00,00,00,000 | One billion |
| Kharab (not normally used) | 1,00,00,00,00,000 | One hundred billion |
| Lakh crore | 10,00,00,00,00,000 | One trillion |
Used withWestern Arabic numerals (0123456789):
Used withEastern Arabic numerals (٠١٢٣٤٥٦٧٨٩):
Used with keyboards:
H command (short for 'hex') displays the entered hexadecimal number in hexadecimal, followed by the same number in decimal, octal, and binary, prefixed with a hash sign (#), backslash (\), and percent sign (%) respectively:-h 12341234 #4660 \011064 %0001.0010.0011.0100
D command (short for 'dump') dumps the memory byte-wise in hexadecimal notation, with bytes separated by spaces and groups of eight bytes separated by hyphens:-d01234:000057696B6970656469-612068656C707321Wikipedia helps!
coma: MAT. Signo utilizado en los números no enteros para separar la parte entera de la parte decimal o fraccionaria; p. ej., 2,123 .
The cost per aircraft was estimated at between N$19,5 million and N$26 million.
La escritura de los números se hará utilizando las cifras arábigas y la numeración decimal, y en ella se separará la parte entera de la decimal mediante una coma (,).
* Write decimal and negative numbers as numerals: 3,3 and –4. Use the decimal comma, not the decimal point: 17,4 million. [...] * Use a space, not commas, to indicate thousands: 3 000, 20 000.
{{cite book}}: CS1 maint: numeric names: authors list (link)The comma is the only recognised decimal indicator for all numbers, including amounts of (currency) money.
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)