A decimal separator is a symbol that separates the integer part from the fractional part of a number written in decimal form. Different countries officially designate different symbols for use as the separator. The choice of symbol can also affect the choice of symbol for the thousands separator used in digit grouping.
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 a dot (either Baseline dot or Middle dot) and comma respectively, when it is used as a decimal separator; these are the usual terms used in English, with the aforementioned generic terms reserved for abstract usage.
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. 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 radix point, a term that also applies to number systems with bases other than ten.
Positional appear for the first time in a book by the Arab mathematician Abu'l-Hasan al-Uqlidisi written in the 10th century.
The practice is ultimately derived from the decimal Hindu–Arabic numeral system used in Indian mathematics,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 work Liber Abaci in the 13th century.
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.
Tables of prepared by John Napier in 1614 and 1619 used the period (full stop) as the decimal separator, which was then adopted by 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.
Many other countries, such as Italy, also chose to use the comma to mark the decimal units position. It has been made standard by the ISO for international blueprints. However, English-speaking countries took the comma to separate sequences of three digits. In some countries, a raised dot or dash ( ) may be used for grouping or decimal separator; this is particularly common in handwriting.
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.
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 advocated for the point. In the event, the point was chosen by the Ministry of Technology in 1968.
When South Africa metrication, it adopted the comma as its decimal separator, although a number of house styles, including some English-language newspapers such as The Sunday Times, continue to use the full stop.
Previously, signs along California roads expressed distances in decimal numbers with the decimal part in superscript, as in 37, meaning 3.7. Though California has since transitioned to with , the older style remains on postmile markers and bridge inventory markers.
Interlingua has used the comma as its decimal separator since the publication of the in 1951.
Esperanto also uses the comma as its official decimal separator, whilst thousands are usually separated by non-breaking spaces (e.g. ). It is possible to separate thousands by a full stop (e.g. ), though this is not as common.
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).
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.Perlis, Alan, The American Side of the Development of ALGOL, ACM SIGPLAN Notices, August 1978. ALGOL ended up allowing different decimal separators, but most computer languages and standard data formats (e.g., C, Java, Fortran, 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).
A radix point is most often used in decimal (base 10) notation, when it is more commonly called the decimal point (with indicating base 10). In 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 ( ·) In many other countries, the radix point is a comma (,) placed on the baseline.
These conventions are generally used both in machine displays (printing, ) and in handwriting. It is important to know which notation is being used when working in different software programs. The respective 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, but, when they are, a radix character may be used for the same purpose. When used with the Binary number (base 2) representation, it may be called "binary point".
That is, "" 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's National Institute of Standards and Technology.
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.
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.
The use of thin spaces as separators instead of dots or commas (for example: and for "twenty thousand" and "one million"), has been official policy of the International Bureau of Weights and Measures (BIPM) since 1948 (and reaffirmed in 2003), as well as of the International Union of Pure and Applied Chemistry (IUPAC), the American Medical Association's widely followed AMA Manual of Style, and the UK Metrication 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". In East Asian cultures, particularly Chinese numerals, Japan, and Korean numerals, large numbers are read in groups of (), but the delimiter often separates the digits into groups of three.
The Indian 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 "".
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) employed commas as the delimiter – 10,000 – and other European countries employed periods (full stops) or spaces: 10.000 or . 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 SI/ISO 31-0 standard, as well as by the BIPM and IUPAC. These groups have also begun advocating the use of a "thin space" in "groups of three".
Within the United States, the American Medical Association's widely followed AMA Manual of Style also calls for a thin space. In programming languages and online encoding environments (for example, ASCII-only languages and environments) a thin space is not practical or available. Often, either underscores and regular word spaces, or no delimiters at all are used instead.
Common examples include and , 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. In web content, digit grouping can be done with CSS. 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 some programming languages, it is possible to group the digits in the program's source code to make it easier to read . Examples include: Ada, C# (since ), D, Go (since ), Haskell (from GHC ), Java, JavaScript (since ES2021), Kotlin, OCaml, Perl, Python (since ), PHP (since ), Ruby, Rust and Zig.
Java, JavaScript, Swift, Julia and free-form Fortran 90 use the underscore () 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 "" would be allowed. In C++14, Rebol and Red, the use of an apostrophe 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:
There are always "common-sense" country-specific exceptions to digit grouping, such as year numbers, , and ID numbers of predefined nongrouped format, which style guides usually point out.
Computer interfaces may be set to the Unicode international "Common locale" using as defined at Details of the current (2020) definitions may be found at
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Notes
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 decimal separator (U+066B, rendered: ) in Unicode. An Arabic thousands separator (U+066C, rendered: ) also exists. Example: (9,999.99)
In Persian language, the decimal separator is called . The Unicode Consortium's investigation concluded that "computer programs should render U+066B as a shortened, lowered, and possibly more slanted slash (); this should be distinguishable from the slash at the first sight." To separate of three digits, an Arabic thousands separator (rendered as: ), a Latin comma, or a blank space may be used; however this is not a standard. Example: (9,999.99)
In English Braille, the decimal point, , is distinct from both the comma, , and the full stop, .
Australia, Cambodia, Canada (English-speaking; unofficial), China, 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. |
Canada (English-speaking; official), China, Estonia (currency numbers), Hong Kong (in education), Mexico, Namibia, South Africa (English-speaking; unofficial), Sri Lanka, Switzerland (in federal texts for currency numbers only), United Kingdom (in education), United States (in education). SI-style (English version), not including currency. |
Albania, Belgium (French), Brazil, Bulgaria, Canada (French-speaking), Costa Rica, Croatia, Czech Republic, Estonia, Finland, 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), Spain (official use since 2010, according to the RAE and CSIC), Sweden, Switzerland (in federal texts, except currency numbers), Ukraine, Vietnam (in education). SI-style (French version), not including currency. |
Austria, Belgium (Dutch), Bosnia and Herzegovina, Brazil (informal and in technology), Chile, Colombia, Croatia (in bookkeeping and technology), Denmark, Germany, Greece, Indonesia, Italy, Latin America (informal), Netherlands, Romania, Slovenia, Serbia, Spain (used until 2010, inadvisable use according to the RAE and CSIC), Turkey, Uruguay, Vietnam. |
Malaysia, Malta, Philippines (uncommon today), Singapore, Taiwan, United Kingdom (older, typically handwritten; in education) |
Bangladesh, India, Nepal, Pakistan . |
Switzerland (computing), Liechtenstein. |
Switzerland (handwriting), Italy (handwriting). |
Spain (handwriting, used until 1980s, inadvisable use according to the RAE and CSIC). |
One | 1 | One |
Ten | 10 | Ten |
Hundred | 100 | Hundred |
Thousand | 1,000 | Thousand |
1,00,000 | One hundred thousand | |
1,00,00,000 | Ten million | |
(not normally used) | 1,00,00,00,000 | One billion |
(not normally used) | 1,00,00,00,00,000 | One hundred billion |
10,00,00,00,00,000 | One trillion |
Used with Eastern Arabic numerals (٠١٢٣٤٥٦٧٨٩):
Used with keyboards:
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