Hubbry Logo
Decimal separatorDecimal separatorMain
Open search
Decimal separator
Community hub
Decimal separator
logo
8 pages, 0 posts
0 subscribers
Be the first to start a discussion here.
Be the first to start a discussion here.
Decimal separator
Decimal separator
Decimal separator
View on Wikipedia
from Wikipedia

Part of a series on
Numeral systems
Place-value notation
Hindu–Arabic numerals
East Asian systems
Contemporary
Historic
Other systems
Ancient
Post-classical
Contemporary
By radix/base
Common radices/bases
Non-standard radices/bases
Sign-value notation
Non-alphabetic
Alphabetic
List of numeral systems
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.
Three ways to group the number ten thousand with digit group separators:
  • 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 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 or middle) and comma 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 or point in most cases.[6][2][7] 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.

History

[edit]

Hellenistic–Renaissance eras

[edit]

In the Middle Ages, before printing, a bar ( ¯ ) over the units digit was used to separate the integral part of a number from its fractional part, as in 9995 (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 9995. Later, a "separatrix" (i.e., a short, roughly vertical ink stroke) between the units and tenths position became the norm among Arab mathematicians (e.g. 99ˌ95), while an L-shaped or vertical bar (|) served as the separatrix in England.[8] When this character was typeset, it was convenient to use the existing comma (99,95) or full stop (99.95) instead.

Positional decimal fractions appear for the first time in a book by the Arab mathematician Abu'l-Hasan al-Uqlidisi written in the 10th century.[9] The practice is ultimately derived from the decimal Hindu–Arabic numeral system used in Indian mathematics,[10] and popularized by the Persian mathematician Al-Khwarizmi,[11] when Latin translation of his work on the Indian numerals introduced the decimal positional number system to the Western world. His Compendious Book on Calculation by Completion and Balancing presented the first systematic solution of linear and quadratic 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 work Liber 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 mathematician Giovanni Bianchini in the 1440s.[13][contradictory]

Tables of logarithms 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.[14]

Many other countries, such as Italy, also chose to use the comma to mark the decimal units position.[14] It has been made standard by the ISO 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.

English-speaking countries

[edit]

In the United States, the full stop or period (.) is used as the standard decimal separator.

The interpunct (·) used as a decimal separator in a British print from 1839[16]

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. 99·95 .[17] 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 Currency Board advocated for the point. In the event, the point was chosen by the Ministry of Technology in 1968.[18]

California milepost marker at mile 144.44

When South Africa adopted the metric system, it adopted the comma as its decimal separator,[19] although a number of house styles, including some English-language newspapers such as The Sunday Times, continue to use the full stop.[citation needed]

Previously, signs along California roads expressed distances in decimal numbers with the decimal part in superscript, as in 37, meaning 3.7.[20] Though California has since transitioned to mixed numbers with common fractions, the older style remains on postmile markers and bridge inventory markers.

Constructed languages

[edit]

The three most spoken international auxiliary languages, 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 Grammar in 1951.[21]

Esperanto also uses the comma as its official decimal separator, whilst thousands are usually separated by non-breaking spaces (e.g. 12 345 678,9). It is possible to separate thousands by a full stop (e.g. 12.345.678,9), though this is not as common.[22]

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).[23]

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.[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).

Radix point

[edit]

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.[25]

A radix point is most often used in decimal (base 10) notation, when it is more commonly called the decimal point (with deci- 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 digits (·)[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 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 number bases, but, when they are, a radix character may be used for the same purpose. When used with the binary (base 2) representation, it may be called "binary point".

Current international standards

[edit]

The 22nd General 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's National Institute of Standards and Technology.[28]

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.[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.

Digit grouping

[edit]

For ease of reading, numbers with many digits (e.g. numbers over 999) may be divided into groups using a delimiter,[30] such as comma (,), dot (.), half-space or thin 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 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, 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 and 1 000 000 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),[27] as well as of the International Union of Pure and Applied Chemistry (IUPAC),[32][33] 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 China, Japan, and Korea, large numbers are read in groups of myriads (10 000s), but the delimiter often separates the digits into groups of three.[citation needed]

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 "10 kharab".[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 or 10 000. 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 SI/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 followed AMA Manual of Style also calls for a thin space.[30] 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[37] and regular word spaces, or no delimiters at all are used instead.

Data vis-à-vis mask

[edit]

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 in spaced groups while not inserting any whitespace 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 (an input mask or an output mask).

Common examples include spreadsheets and databases, 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:

  • 149597870700 metres is 1 astronomical unit.
  • 3.14159265358979323846 is π rounded to 20 decimal places.
  • 2.71828182845904523536 is e rounded to 20 decimal places.

In many programming languages, it is possible to group the digits in the program's source code to make it easier to read (see: Integer literal § Digit separators).

Ada, Free-form Fortran 90, Perl, D, OCaml, Ruby, Java, Rust, Julia, Python (since version 3.6), Kotlin[38], C# (since version 7.0)[39], Swift, Haskell (from GHC version 8.6.1), Go (since version 1.13), PHP (since version 7.4),[40], Zig[41], and JavaScript (since ES2021) have adopted 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 "700 000 000" 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: 

val exampleNumber = 12_000_000 // twelve million

Exceptions to digit grouping

[edit]

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, some manuals of style state that thousands separators should not be used in normal text for numbers from 1000 to 9999 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 of 1000 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 non-base-10 numbering systems

[edit]

In binary (base-2), a full space can be used between groups of four digits, corresponding to a nibble, or equivalently to a hexadecimal 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 an octal digit. Similarly, in hexadecimal (base-16), full spaces are usually used to group digits into twos, making each group correspond to a byte.[c] Additionally, groups of eight bytes are often separated by a hyphen.[c]

Influence of calculators and computers

[edit]

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 as electronic calculators, which use the decimal point. Most computer operating systems allow selection of the decimal separator; programs that have been carefully 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 LC_NUMERIC=C as defined at "Unicode CLDR project". Unicode Consortium. Details of the current (2020) definitions may be found at "01102-POSIX15897". Unicode Consortium.

Conventions worldwide

[edit]
Decimal separators:
  Dot (.)
  Comma (,)
  Both (may vary by location or other factors)
  Arabic decimal separator (٫‎)
  Data unavailable

Hindu–Arabic numerals

[edit]

Countries using decimal comma

[edit]

Countries where a comma (,) is used as a decimal separator include:

  • Albania
  • Algeria
  • Andorra
  • Angola
  • Argentina
  • Armenia
  • Austria
  • Azerbaijan
  • Belarus
  • Belgium
  • Bolivia
  • Bosnia and Herzegovina
  • Brazil
  • Bulgaria[i]
  • Cabo Verde
  • Cameroon
  • Canada (when using French)
  • Chile
  • Colombia
  • Costa Rica
  • Croatia
  • Cuba
  • Cyprus
  • Czech Republic
  • Denmark
  • East Timor
  • Ecuador
  • Estonia
  • Faroes
  • Finland
  • France
  • Germany
  • Georgia
  • Greece
  • Greenland
  • Hungary
  • Iceland
  • Indonesia
  • Italy
  • Kazakhstan
  • Kyrgyzstan
  • Laos
  • Latvia
  • Lebanon
  • Lithuania
  • Luxembourg
  • Macau (in Portuguese text)
  • Mauritania
  • Moldova
  • Mongolia[i]
  • Montenegro
  • Morocco
  • Mozambique
  • Namibia (uses both marks)[42]
  • The Netherlands
  • North Macedonia
  • Norway
  • Paraguay
  • Peru[43]
  • Poland
  • Portugal
  • Romania
  • Russia
  • San Marino
  • Serbia
  • Slovakia
  • Slovenia
  • Somalia
  • South Africa[44][45]
  • Spain[ii]
  • Suriname
  • Sweden[ii]
  • Switzerland[iii]
  • Tunisia
  • Turkey
  • Turkmenistan
  • Ukraine
  • Uruguay
  • Uzbekistan
  • Venezuela
  • Vietnam
  • Zimbabwe

Countries using decimal point

[edit]

Countries where a dot (.) is used as a decimal separator include:

  • Australia
  • Bahamas, The
  • Bangladesh
  • Botswana
  • British West Indies
  • Cambodia
  • Canada (when using English)
  • China
  • Cyprus (currency numbers)
  • Dominican Republic
  • Egypt
  • El Salvador
  • Ethiopia
  • Ghana
  • Guatemala
  • Guyana
  • Honduras
  • Hong Kong
  • India
  • Ireland
  • Israel
  • Jamaica
  • Japan
  • Jordan
  • Kenya
  • Korea, North
  • Korea, South
  • Libya
  • Liechtenstein
  • Macau (in Chinese and English text)
  • Malaysia
  • Maldives
  • Malta
  • Mexico
  • Myanmar
  • Namibia (uses both marks)
  • Nepal
  • New Zealand
  • Nicaragua
  • Nigeria
  • Pakistan
  • Panama
  • Peru (currency numbers)
  • Philippines
  • Qatar
  • Saudi Arabia
  • Singapore
  • Somalia
  • Sri Lanka
  • Switzerland[iii]
  • Syria
  • Taiwan
  • Tanzania
  • Thailand[ii]
  • Uganda
  • United Arab Emirates
  • United Kingdom
  • United States (including insular areas)

Notes

  1. ^ a b The national literary convention in Bulgaria and Mongolia is to use the comma as a decimal separator, but many places use the dot instead due to the prevalence of imported technology that internally uses the dot as the decimal separator. This is because the technology usually utilizes the decimal separator conventions of the country it was made in, and most of the technology is made in the United States, countries following the conventions and standards (such as ASCII) of the United States, or China – all of which use the dot as a decimal separator. Thus, in Bulgaria, the comma is the conventional decimal separator, but both the comma and the dot are used in practice. This is true for Mongolia as well, but the dot is more commonly used instead.
  2. ^ a b c According to several software developers, Spain and Sweden both use a comma as a decimal separator while Thailand uses a dot instead.[48][49]
  3. ^ a b The decimal point is used in some cantons of Switzerland (for example the Canton of St. Gallen[46]). It is used in IT and with currency values. On the other hand, the decimal comma is used in federal publications[47] and some other cantons.

Other numeral systems

[edit]

Unicode defines a decimal separator key symbol (⎖ in hex U+2396, decimal 9110) which looks similar to the apostrophe. This symbol is from ISO/IEC 9995 and is intended for use on a keyboard to indicate a key that performs decimal separation.

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: ۹٬۹۹۹٫۹۹‎ (9,999.99)

In Persian, the decimal separator is called momayyez. 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 sequences 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.[50][51][52] Example: ۹٬۹۹۹٫۹۹ (9,999.99)

In English Braille, the decimal point, ⠨, is distinct from both the comma, ⠂, and the full stop, ⠲.

Examples of use

[edit]

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,[53][54] Cambodia, Canada (English-speaking; unofficial), China,[55] 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,[55] Estonia (currency numbers), Hong Kong (in education), Mexico, Namibia, South Africa (English-speaking; unofficial), Sri Lanka, Switzerland (in federal texts for currency numbers only[56]), 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,[57] 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[58]), Spain (official use since 2010, according to the RAE and CSIC), Sweden, Switzerland (in federal texts, except currency numbers[56]), Ukraine, Vietnam (in education). SI-style (French version), not including currency.
1.234.567,89 Austria, Belgium (Dutch), Bosnia and Herzegovina, Brazil (informal and in technology), Chile, Colombia, Croatia (in bookkeeping and technology),[59] Denmark, Germany, Greece, Indonesia, Italy, Latin America (informal), Netherlands, Romania, Slovenia, Serbia, Spain (used until 2010, inadvisable use according to the RAE and CSIC),[d][61] 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 the RAE and CSIC).[62]
  • In Belgium (Dutch), Brazil, Denmark, Germany, Greece, Indonesia, Italy, Netherlands, Portugal, Romania, Russia, Slovenia, Sweden and much of Europe, "1234567,89" or "1.234.567,89" are seen. In handwriting, "1˙234˙567,89" 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: "1'234'567,89". 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.[63]
  • In Estonia, currency numbers often use a dot (.) 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.
  • Historically, in Germany and Austria, thousands separators were occasionally denoted by alternating uses of commas and points, e.g. "1.234,567.890,12" (or "1.234,567.890·12" in Austo-Hungary and Austria prior to 1938)[64][65][66] for "eine Milliarde 234 Millionen ...", but this isn't seen today and contemporary German readers would require an explanation to understand it.
  • In Switzerland, there are two styles. Currency values use an apostrophe (') 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".
  • In Ireland, Israel, Japan, Korea (both), Malaysia, the Philippines, Singapore, Taiwan, Thailand, the United Kingdom, and the United States, "1,234,567.89" or "1,234,567·89" are seen. However, the latter is generally only found in older, handwritten documents.
  • For English-speaking regions of Canada, there are two styles. The preferred style for currency values is "$10,000.00", while the preferred style for numeric values is "1234567.89". However, commas are also sometimes used, despite no longer being taught in school or used in official publications.[citation needed]
  • The International System of Units (SI) uses the following two styles: "1234567.89" and "1234567,89". In their own publications, a dot (.) is used in the English version, while a comma (,) is used in the official French version.
  • In Sweden, a colon (:) is sometimes used as the decimal separator for currency values, like "1 234 567:89".
  • In China, commas and spaces are used to mark digit groups, since dots are used as decimal separators. There is no universal convention on digit grouping, however, so both thousands grouping and no digit grouping can be found. Japan and Taiwan are similar, although, when grouping by myriads, kanji or Chinese characters are frequently used as separators, like the following: "1億2345万6789" or "1億2345萬6789" (see Japanese numerals and Chinese numerals). Commas are used when grouping by thousands.
  • In India, which uses the Indian numbering system, commas (,) are used at the thousands, lakh, and crore levels. For example, 10 million (1 crore) would be written "1,00,00,000", while 100 thousand (1 lakh) would be written "1,00,000". In Pakistan, there is a greater tendency to use the standard western system, but the Indian numbering system is used when conducting business in Urdu.
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

Unicode characters

[edit]

Used with Western Arabic numerals (0123456789):

  • U+0020   SPACE
  • U+0027 ' APOSTROPHE (')
  • U+002C , COMMA (,)
  • U+002E . FULL STOP (.) - Full stop punctuation mark.
  • U+00B7 · MIDDLE DOT (·, ·, ·)
  • U+2009   THIN SPACE ( ,  )
  • U+202F   NARROW NO-BREAK SPACE
  • U+02D9 ˙ DOT ABOVE (˙, ˙)
  • U+005F _ LOW LINE (_, _) - Underscore

Used with Eastern Arabic numerals (٠١٢٣٤٥٦٧٨٩):

  • U+066B ٫ ARABIC DECIMAL SEPARATOR
  • U+066C ٬ ARABIC THOUSANDS SEPARATOR

Used with keyboards:

  • U+2396 ⎖ DECIMAL SEPARATOR KEY SYMBOL (resembles an apostrophe)

See also

[edit]

Footnotes

[edit]

References

[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Decimal separator

View on Grokipedia
from Grokipedia
A decimal separator is a symbol used to separate the part from the of a number written in decimal notation, also referred to as the character or decimal marker. The two most common s are the dot (.) placed on the baseline and the (,) raised slightly or on the baseline, with usage determined by linguistic and regional conventions. For example, the number three point one four is written as 3.14 in English-speaking countries like the and the , but as 3,14 in many European nations such as , , and . International standards organizations recognize both symbols to accommodate global diversity in numerical formatting while promoting clarity in scientific and technical communication. The International Bureau of Weights and Measures (BIPM), through resolutions of the General Conference on Weights and Measures (CGPM), specifies that the decimal marker may be either a point or a comma on the line, with English-language SI publications favoring the dot and French-language ones using the . Similarly, the ISO/IEC Directives, Part 2, recommend the as the decimal sign in all language versions of standards documents to ensure consistency, while allowing flexibility in non-standard contexts. Regional variations persist today, with the as decimal separator prevalent in most of , , and parts of and Asia, whereas the dot dominates in the , , , and international . In some locales, such as , both symbols may appear contextually, with the for general numbers and the dot for currencies. These differences underscore the importance of locale-aware formatting in global data exchange to maintain accuracy and readability. The dot's use as a decimal separator traces back to the in English mathematical texts, while the comma gained prominence in during the 18th and 19th centuries, partly to avoid confusion with the dot's emerging role in notation.

Basic Concepts

Definition and Purpose

A decimal separator, also known as a decimal point or decimal mark, is a employed in for base-10 numbers to delineate the part from the . This symbol, typically a period (.) or (,), serves as the character that marks the boundary between the whole number and its expansion. The primary purpose of the decimal separator is to enable the clear representation and manipulation of decimal fractions, thereby supporting precise numerical computations and readability in various domains. It is indispensable for applications requiring accuracy, such as measurements in science and (e.g., 1.5 meters for ), financial transactions (e.g., $3.99 for ), and everyday quantifications where fractions of a unit must be expressed without . By indicating the onset of fractional values, it facilitates operations like , , and division while minimizing errors in interpretation. For instance, the approximation of π as 3.14 uses the period as the separator in Anglo-American conventions, whereas 3,14 employs the in many European locales. fractions were systematically promoted in the by in his 1585 treatise De Thiende using an alternative notation with circled digits, while the modern decimal separator developed later. Mathematically, a decimal expression such as a.ba.b, where aa denotes the part and bb the digits of the with nn places, equates to a+b10na + \frac{b}{10^n}. More generally, it forms part of the expansion ∑kdk×10k\sum_k d_k \times 10^k, where dkd_k are digits (0-9), positive exponents apply to the portion, and negative exponents to the fractional, with the separator at the 10010^0 position. This structure underpins the base-10 system's ability to approximate real numbers with arbitrary precision.

Distinction from Thousands Separator

The decimal separator serves to divide the part of a number from its , indicating the position of the decimal place, as in the English convention of 1,234.56 where the period (.) marks the boundary between 1,234 and 56. In contrast, the thousands separator, also known as the digit grouping separator, is used solely to enhance readability by grouping digits within the integer portion, typically every three digits from the right, as in the same example where the (,) separates 1 from 234. These roles are fundamentally non-interchangeable: the decimal separator defines numerical precision, while the thousands separator provides visual structure without altering the value. Formatting conventions reinforce this distinction. The decimal separator always appears immediately after the integer part and before any fractional digits, with no repetition. The thousands separator, however, is placed within the integer part, repeating at fixed intervals (usually every three digits) and omitting from the fractional part entirely. International standards, such as those in the SI Brochure, recommend using a for thousands grouping to avoid overlap with decimal symbols, explicitly prohibiting the use of periods or commas in that role. Despite these clear functions, overlap in symbol usage across locales can create . In regions employing the as a decimal separator, such as or , a period often serves as the thousands separator, resulting in notations like 1.234,56—which could be misread as one thousand two hundred thirty-four point five six in point-decimal conventions. This inversion heightens risks in cross-border contexts, where the same string might represent vastly different values depending on interpretation. Such confusion manifests notably in and , where locale-specific number formats in documents or data files can lead to errors. For instance, a French-formatted amount like ,00 might be erroneously processed as about 429 billion in a U.S. system expecting comma-thousands and point-decimal, potentially causing significant financial discrepancies during currency conversions or . To mitigate this, global standards emphasize consistent application within documents and the use of non-ambiguous separators like spaces for grouping.

Historical Development

Ancient and Medieval Origins

The concept of a decimal separator emerged from early efforts to represent fractional parts in positional numeral systems, predating modern decimal notation. In the Hellenistic era, during the 2nd century AD, the astronomer introduced for fractions in his seminal work , employing a (base-60) system as a precursor to decimal methods. used horizontal overlines or bars placed above sequences of digits to denote the onset of the fractional portion, distinguishing it from the integer part and enabling precise astronomical calculations without relying on common fractions. During the medieval Islamic Golden Age, significant advancements in decimal positional notation occurred, building on Indian influences. In the 10th century, the mathematician Abu'l-Hasan al-Uqlidisi (c. 920–980) pioneered the explicit use of decimal fractions in his treatise Kitab al-Fusul fi al-Hisab al-Hindi (Book of Chapters on Hindu Arithmetic), completed in 952–953 AD. Al-Uqlidisi employed a dedicated decimal sign—resembling a small elevated comma or apostrophe (' )—to separate the integer from the fractional digits, facilitating operations like multiplication and division on paper rather than dust boards. This innovation marked the first consistent application of a separator for decimal fractions, emphasizing their utility in practical computations such as inheritance divisions. In the period, European scholars began advocating for decimal fractions, drawing indirectly from Islamic sources. Flemish mathematician (1548–1620) played a key role in 1585 with his pamphlet La Thiende (The Tenth), where he promoted the use of decimal fractions for applications in astronomy, , and commerce to simplify measurements and eliminate cumbersome vulgar fractions. Stevin initially denoted fractional places with small superscript circles (e.g., ⓪ for units, ① for tenths) placed to the right of the digits, though he also experimented with points as separators, arguing for their adoption to streamline arithmetic across trades like minting and gauging. Prior to the widespread adoption of printing in Europe around the mid-15th century, decimal separators saw limited but innovative use in specialized fields. In the 1440s, Venetian merchant and astronomer Giovanni Bianchini (d. 1469) incorporated dots as decimal points in his manuscript astronomical tables, Tabulae primi mobilis, to compute sine values and planetary positions with decimal fractions (e.g., tenths and hundredths). This notation, appearing in interpolation columns for trigonometric functions, supported both scholarly astronomy and mercantile calculations, predating printed works and highlighting early practical integration in Italian intellectual circles.

Modern Standardization Efforts

In the 19th century, English-speaking countries solidified the use of the decimal point (.) as the standard separator for decimal fractions, building on earlier mathematical traditions from figures like and . By the mid-1800s, the low-placed dot had become nearly universal in the United States, reflecting a preference for clarity in scientific and commercial printing that distinguished it from potential symbols or other . This adoption was influenced by practical needs in expanding industrial and contexts, where consistency aided calculations in and . In Britain, while the elevated dot was recommended by in 1795 to avoid ambiguity, the low dot gained traction by the late 19th century, as seen in works by authors like in 1911. In , particularly and , the decimal (,) emerged as the dominant convention by the mid-19th century, shaped by typographic practices that reserved the point for separating or other notations. French mathematicians such as in 1815 and Jean-Baptiste Joseph Fournier in 1842 consistently employed the low in logarithmic and fractional expressions, aligning with broader printing standards that favored the for readability in dense texts. Similarly, in , Georg Simon Ohm's 1829 electrical series used the . This widespread European preference for the stemmed from its distinction from the point's established roles, facilitating uniform notation in academic publications across these nations. Early 20th-century efforts toward unification highlighted persistent divisions, as evidenced by the mixed usage of points and commas at the International Mathematical Congress in in 1920, where delegates from various countries presented notations without achieving consensus. These talks reflected growing awareness of notation's impact on cross-border precision in measurements and trade, though formal resolutions allowing both symbols were not adopted until the 9th CGPM in 1948. Constructed international languages from the late , such as (introduced in 1887 by ) and (developed in 1907 as a of Esperanto), adopted the to promote accessibility and consistency for global users, aligning with prevailing European conventions while aiming for neutrality in auxiliary communication. In , the serves as the official decimal marker, with thousands grouped by spaces or apostrophes, as standardized in its orthographic guidelines to facilitate mathematical and scientific expression among speakers. followed suit, using the to mirror this inclusive approach in its simplified .

Terminology Evolution

The terminology for the decimal separator has evolved alongside the development of positional numeral systems, reflecting both linguistic preferences and efforts toward mathematical generalization. In English-speaking contexts, the term "decimal point" emerged in the 17th century, following John Napier's introduction of the period (.) as a separator in his 1616 work Mirifici Logarithmorum Canonis Descriptio, which became standard in England by 1619. In French mathematical literature, the equivalent term "virgule décimale" (decimal comma) appeared in older texts to describe the comma (,) usage, with "comma décimale" gaining prominence in the 18th century as the symbol solidified in continental European practice. To accommodate numeral systems beyond base 10, the synonym "" was coined in the mid-20th century as a neutral term for the separator in any (base), generalizing the concept from the base-10-specific "decimal point." This shift emphasized universality in and computing, where the separator divides the and fractional parts regardless of the base. Regional variations persist in nomenclature; for instance, Spanish texts refer to it as "punto decimal" when using the dot, though "coma decimal" is common in comma-using regions. International standardization bodies addressed terminological debates in the by adopting neutral phrasing to avoid symbol-specific bias. The (ISO), in standards like ISO 31-0 (first published in 1978 and revised through the ), referred to the separator as the "decimal sign," specifying it as a comma on the line while allowing regional variations, to promote clarity in multilingual technical documents. This approach influenced subsequent guidelines, such as those from the General Conference on Weights and Measures (CGPM), which in 1948 recognized both (French practice) and dot (British practice) without favoring one in terminology.

Global Conventions

Regions Using Decimal Point

The decimal point, represented by a period (.), serves as the standard decimal separator in numerous countries worldwide, particularly those influenced by Anglo-American conventions, as reflected in currency formatting standards aligned with international practices. This usage is prevalent in English-speaking nations such as the , , (in English contexts), and , where it has been conventional since the , stemming from British typographic traditions that favored the point for clarity in printed mathematical and commercial texts. In French-speaking parts of , such as , the comma is commonly used, though federal standards align with the point. In addition to these core regions, the decimal point is standard in several Asian countries including , , and , as well as and other parts of the like the . The preference for the point in these areas often traces back to historical ties with British colonial influences or U.S. commercial during the expansion of global in the 19th and 20th centuries, which promoted consistent formatting for international transactions. Notable exceptions exist within these regions; for instance, employs the decimal point for fractions but follows a unique digit-grouping system for large integers, typically separating the rightmost three digits with a and subsequent pairs with spaces or additional commas (e.g., 12,34,56,789), diverging from the standard Western three-digit grouping. This hybrid approach accommodates the , which uses terms like and for scales beyond thousands. Examples of countries using the decimal point include:
Region/CategoryRepresentative Countries
English-speaking, , (English), ,
Asia-Pacific, , , , ,
Americas, , (French contexts vary but align in federal standards)
OtherBotswana, Brunei, Israel, South Korea, Thailand
This distribution covers numerous sovereign states and territories, as indicated by locale data for numeric formatting in global software standards. In some countries like , while the point is common in English contexts, the official standard uses the .

Regions Using Decimal Comma

The use of the comma (,) as a decimal separator is prevalent in numerous countries, particularly across , , and parts of and the . In , countries such as , , , , and employ the comma to distinguish the integer part of a number from its fractional part, a convention that extends to official documents, education, and commerce. Similarly, in , nations including and adopt this format, reflecting colonial influences from European powers like and . This practice is also common in several countries, such as and (in official metric contexts), and in Middle Eastern regions like and , where it aligns with regional linguistic and historical norms. The adoption of the decimal comma traces back to continental European mathematical traditions, emerging prominently in 18th- and 19th-century texts where the comma served as a marker for fractional values, evolving from its earlier role in denoting proportions in arithmetic and . This usage gained traction as mathematicians sought a consistent symbol to separate decimal places, contrasting with the point favored in Anglo-American contexts, and became standardized in educational materials across by the late 19th century. The convention spread through colonial and trade networks, influencing Latin American and African nations during the 19th and 20th centuries as they formalized metric systems and national standards. Globally, the decimal comma is used in over 100 countries, encompassing the majority of members—such as , , and —and aligning with many member states in , , and beyond. This widespread prevalence supports regional , as seen in the European Union's emphasis on localized number formatting for data interoperability. However, it poses challenges in international contexts, particularly when exporting numerical data in formats like CSV files, where software defaults to the decimal point can lead to misinterpretation of values— for instance, 1,25 being parsed as 125 instead of 1.25—requiring manual adjustments or locale-specific settings to avoid errors in cross-border trade and scientific exchange.

Alternative Separators in Other Systems

In numeral systems other than base-10, the boundary between the and fractional parts is denoted by the radix point, which functions analogously to the decimal separator but accommodates the specific base of the notation. In binary (base-2) and (base-16) representations, commonly used in , the radix point is typically a period (.), mirroring its role in decimal systems. For instance, the binary value 10.11₂ equals 1.75₁₀, as the fractional portion .11₂ breaks down to 1×2⁻¹ + 1×2⁻² = 0.5 + 0.25 = 0.75. Similarly, hexadecimal fractions like 1A.8₁₆ represent values such as 26.5₁₀, with the radix point separating the integral 1A₁₆ (26₁₀) from the fractional 0.8₁₆ (0.5₁₀). In non-Latin scripts, decimal separators adapt to local numeral forms while often retaining the point for compatibility. Eastern Arabic numerals (٠١٢٣٤٥٦٧٨٩), used in Arabic-speaking regions and Persian contexts, employ the dedicated Arabic decimal separator ٫ (U+066B) to distinguish the fractional part, as in ٣٫١٤ for π ≈ 3.14; the Western period (.) or comma (,) serves as an alternative in mixed or international settings. Chinese numeral systems, which blend traditional characters (e.g., 一二三) with Arabic digits for modern use, standardize the decimal point (.) as the separator, pronounced "diǎn" (点), yielding forms like 3.14 for π regardless of whether Arabic or rod numerals are employed. Historically, alternatives to or appeared in 18th-century European mathematical texts, where spaces were also employed sporadically as separators in early fractional notations before standardization. In older , the middle dot (·) functioned as a decimal marker, particularly in British publications, to differentiate it from the multiplication symbol, as in 23·4 for 23.4.

Standards and Guidelines

International Recommendations

The International Bureau of Weights and Measures (BIPM), which maintains the (SI), established guidelines for decimal separators to promote consistency in scientific measurements. Resolution 7 of the 9th General Conference on Weights and Measures (CGPM) in 1948 permitted either the (as per French practice) or the dot (as per British practice) exclusively to separate the integral part from the decimal part of numbers, avoiding their use for other purposes like digit grouping. This dual acceptance was reaffirmed and clarified in Resolution 10 of the 22nd CGPM in 2003, stating that the decimal marker "shall be either the point on the line or the on the line," with the choice depending on the language of the text—typically the point in English publications and the in French ones—to support global scientific communication without mandating a single symbol. The SI Brochure, updated in 2019, echoes this flexibility while exemplifying the decimal point in English contexts for numerical values in scientific writing. The (ISO) addresses decimal separators in ISO 80000-1:2009, "Quantities and units—Part 1: General," which specifies that the decimal sign shall be either a or a point on the line, chosen consistently within a document to avoid ambiguity. This standard emphasizes customary practices, noting the decimal point for English-language texts and the for French, but encourages the point in international mathematical expressions to enhance across borders. The 2022 revision maintains this approach, prioritizing clarity in quantities and units for technical and scientific applications without enforcing a universal preference, thereby aiding unification in global standards. In the domain of electronics and , the (IEC) has evolved its conventions to facilitate international technical documentation. Prior to 2006, IEC standards required the comma as the decimal separator, but following alignment with ISO and input from the CGPM, the organization approved the use of the decimal point in English-language publications that year, reflecting the needs of major economies like the , , , and . This shift, implemented through joint ISO/IEC directives, supports binary and decimal in computing standards such as ISO/IEC 60559:2020, where the point is used in examples and specifications to streamline interchange formats and reduce errors in global software and hardware development. The (UN) and promote adaptable guidelines for decimal separators in educational and official contexts to bridge linguistic divides, while favoring the point in English documentation for consistency. The UN Editorial Manual requires the decimal point for fractions, including a for values less than one (e.g., 0.5), to ensure precise representation in reports and resolutions. 's correspondence manual similarly mandates the decimal point for decimals (e.g., 7.4), allowing flexibility in multilingual educational materials but standardizing the point in official English texts to align with international scientific norms. These policies underscore broader unification efforts by accommodating regional variations in teaching while prioritizing the point for cross-border official use.

National and Regional Variations

In the , the National Institute of Standards and Technology (NIST) recommends the dot on the line as the decimal separator to distinguish whole numbers from fractional parts, a convention strictly followed in federal documents to ensure consistency in scientific and technical communications. This adherence to the decimal point aligns with broader efforts to harmonize U.S. practices with international standards while avoiding the decimal comma in official contexts. Similarly, in the , the decimal point is the standard separator in English-language usage for both everyday and official purposes, reflecting shared conventions with the . Across countries, the decimal comma serves as the official separator in most national standards, promoting uniformity in administrative and commercial documents. For instance, in , DIN 5008 specifies the comma as the decimal marker, such as in expressions like 12,50 euros, which is the norm for textual and financial writing. These national implementations often diverge from international recommendations by prioritizing the comma for local readability, though both symbols are acknowledged globally. In Asia, countries like and predominantly employ the point in standard numerical notation, aligning with international scientific practices. uses the period as the for decimals, as seen in educational and technical materials where numbers like 1.3 are read with "ten" indicating the point. In , the point is standard for fractional values, while commas are reserved for thousands grouping, though traditional lakh-crore systems in local scripts may influence informal thousand separations without affecting the decimal convention. Several African nations have adopted the decimal point following colonial influences and to facilitate , particularly in English-speaking regions. For example, countries such as and use the point as the decimal separator in official and commercial contexts, reflecting post-independence alignment with global economic standards. In contrast, nations like retain the decimal comma, illustrating regional variations shaped by diverse linguistic and historical factors.

Digit Grouping Practices

Common Grouping Symbols

Digit grouping, also known as thousands separation, is a convention used to divide the digits of into groups to improve , particularly for integers exceeding a few digits. This practice reduces by allowing readers to quickly parse the scale and magnitude of numbers, such as distinguishing 1000000 from at a glance. Without grouping, long sequences of digits can appear as dense blocks, increasing the error rate in mental estimation and comprehension. Grouping typically occurs every three digits, starting from the rightmost digit in the part and proceeding leftward, forming clusters that align with the base-10 place value . For example, the number 1234567 would be formatted as 1,234,567 in conventions using a . This triadic grouping reflects the natural human tendency to process information in sets of three, enhancing visual scanning efficiency. Common symbols for digit grouping vary by locale and reflect historical, linguistic, and typographic influences. In the United States and other English-speaking countries following Anglo-American conventions, the comma (,) serves as the standard thousands separator, as seen in 1,000,000. In Germany, a period (.) is frequently used for this purpose, resulting in formats like 1.000.000, which avoids confusion with the comma employed as a decimal marker. France and several other European nations prefer a thin space (U+2009), non-breaking space (U+00A0), or narrow non-breaking space (U+202F) to separate groups, yielding 1 000 000, a choice that maintains neutrality in symbol usage. Switzerland and Liechtenstein adopt the apostrophe (') as their grouping symbol, producing 1'000'000, a tradition influenced by both Germanic and Romance linguistic regions within the country. International standards, such as ISO 80000-1, recommend grouping digits in threes from the decimal sign using a for scientific and technical contexts to ensure clarity across borders, though they acknowledge that locale-specific symbols like the or period are permissible in everyday use. This flexibility allows adaptation to regional norms while promoting consistency in global communication, such as in financial reports or documents.

Integration with Decimal Separators

In regions adhering to the decimal point convention, such as the and the , the thousands separator is typically a , while the decimal separator is a period, resulting in formats like 1,234.56 for one thousand two hundred thirty-four and fifty-six hundredths. Conversely, in many European countries following the decimal convention, including , the decimal separator is a , and the thousands separator is often a or period, yielding formats such as 1 234,56 or 1.234,56. These locale-specific rules ensure clarity within cultural contexts but can lead to confusion in international exchanges, where mismatched separators might misinterpret 1,000.50 as one thousand point five zero in point-decimal locales or one point zero zero zero point five zero in -decimal ones. To resolve potential ambiguities, particularly in scientific and technical writing, international standards recommend using a thin space as the thousands separator regardless of the decimal marker, avoiding commas or points that could conflict with decimal notation. For instance, the International System of Units (SI) specifies grouping digits in threes around the decimal marker with a thin space for numbers exceeding four digits on either side, such as 1 234 567,89, while prohibiting dots or commas in these spaces to maintain universality. In contexts where even this might cause issues, such as inline mathematical expressions, no grouping separator is used at all to prioritize precision over readability. Software applications often enforce these integrations through locale-aware data masks and regional settings to prevent input errors and ensure consistent output. In , for example, users can configure decimal and thousands separators via system regional settings or override them in the Advanced options under File > Options, where unchecking "Use system separators" allows custom entry like a period for decimals and for thousands in U.S. locales, automatically applying formats such as 1,000.00. This adaptability aligns with broader standards, enabling seamless handling of mixed notations in global spreadsheets without manual reformatting.

Exceptions and Non-Standard Uses

In non-base-10 numeral systems, digit grouping conventions deviate from the standard decimal practices to align with binary representations or computational efficiency. For binary numbers, bits are commonly grouped into sets of 8, known as bytes, and displayed with spaces between these groups for , such as 10110110 01101001 to represent two consecutive bytes. In notation, which represents 4 bits per digit, numbers are often grouped every 4 digits (equivalent to 16 bits or a word), separated by colons, as seen in addresses like 2001:0db8:0000:0000:0000:ff00:0042:8329. Certain cultural and contextual exceptions further illustrate irregular grouping. The Indian numbering system employs a unique pattern where the rightmost three digits form the units to thousands group, followed by pairs of two digits for higher places like lakhs (100,000s) and crores (10,000,000s), using commas accordingly—for instance, 12,34,56,789 represents twelve crores, thirty-four lakhs, fifty-six thousand, seven hundred eighty-nine. In contrast, compact notations such as financial stock ticker symbols avoid any digit grouping to preserve brevity; these are typically 1 to 6 alphanumeric characters, like UNP for Union Pacific or numeric codes in some Asian exchanges, ensuring quick identification without separators. Digital interfaces often distinguish between display formatting and computational storage to maintain accuracy. Input masks in forms, such as those in , enforce visible grouping (e.g., commas for thousands) during user entry for clarity, but the stored value excludes these mask characters—using a specifier like ";1"—allowing seamless numerical computations without overhead. Rare symbols provide additional non-standard options for grouping in programming contexts. Since Python 3.6, underscores (_) have been permitted as visual separators in numeric literals across bases, improving readability without affecting the parsed value; examples include 1_000_000 for one million in decimal or 0xCAFE_F00D in hexadecimal, where the underscores are ignored during evaluation.

Technological Influences

Calculators and Early Computing

The development of mechanical calculating devices, particularly slide rules prevalent before the 1940s, significantly influenced decimal separator conventions by necessitating manual alignment for fractional parts. Users of linear slide rules had to mentally position the decimal point, as the scales lacked explicit markers for numbers greater than 10 or less than 1, relying on the cursor or index lines for approximate alignment during logarithmic operations. Some advanced models incorporated auxiliary scales or etched alignment lines to assist in decimal placement, ensuring consistency in engineering and scientific computations without a physical separator symbol. In the 1960s, early electronic calculators from U.S. manufacturers like (TI) and (HP) standardized the decimal point as the separator, driven by domestic conventions in manufacturing and design. The TI Datamath, introduced in 1972 as one of the first handheld solid-state calculators, featured a dedicated decimal point key and displayed results with a dot separator for up to 12 digits, reflecting American numerical formatting. Similarly, HP's 9100A desktop calculator, released in 1968 and marketed as the world's first programmable , used the decimal point exclusively in its input and output interfaces, embedding the U.S. standard into hardware architecture. These designs prioritized compatibility with American engineering practices, where the point had long been the norm. The (ANSI) further reinforced this preference through its standardization efforts in computing hardware during the 1960s. The ANSI X3.4-1968 standard, codifying the ASCII character set which includes the period (.), supported the conventional use of the period as the decimal separator in interchange, influencing hardware manufacturers to adopt it universally in displays and keypads to ensure . This push aligned with broader initiatives by the Computer and Business Equipment Manufacturers Association (CBEMA), which collaborated with ANSI to promote consistent numerical representation in electronic systems. The widespread export of these U.S.-manufactured calculators in the late and contributed to the spread of the decimal point as an in technical education and industry.

Software and Programming Conventions

In programming languages such as C++ and , floating-point literals are defined using the decimal point (.) as the separator between the and fractional parts, regardless of the system's locale settings. For example, the literal 3.14 represents the value three point one four in , ensuring consistent across environments. This convention stems from the languages' lexical specifications, which mandate the ASCII period character for decimal points to maintain portability and avoid ambiguity in code compilation. Python, in contrast, provides locale-aware formatting for decimal numbers through its locale module and string formatting methods. The locale.format() function or the format() method with a locale specifier adjusts the decimal separator based on the current locale—for instance, using a (,) in locales like German (de_DE) while defaulting to a point (.) in others like English (en_US). This allows developers to output numbers in a culturally appropriate manner without altering the underlying binary representation, which remains locale-independent. The (ICU) library addresses internationalization challenges by providing robust parsing and formatting for decimal numbers across locales. ICU's DecimalFormat class automatically handles varying decimal separators, such as points or commas, during input parsing and output generation, ensuring correct interpretation of numeric strings from different regions. For example, it can parse "3,14" as 3.14 in a European locale while formatting the same value as "3.14" for export in a context, reducing errors in global applications. The standard for specifies formats for both binary and decimal representations but does not directly govern syntax; however, implementations in programming languages consistently use the decimal point in literals to align with the standard's interchange formats, which employ the point for decimal notation in textual representations. This uniformity in binary floating-point handling ensures that values like 3.14 are encoded identically across compliant systems, independent of locale-specific display preferences. A common issue arises in CSV exports, where locale-dependent decimal separators can lead to parsing errors if the file is opened in a system with differing conventions—for instance, a value written as "3,14" in a comma-using locale may be misinterpreted as 314 in a point-using environment like standard Excel. Developers must often perform explicit locale conversion during , such as replacing commas with points and quoting fields, to ensure universal compatibility and prevent data corruption.

Digital Interfaces and User Experience

In web standards, the requires the period (.) as the decimal separator for valid numerical input, as outlined in the HTML Living Standard, to ensure uniform browser parsing regardless of user locale. This approach prioritizes backend consistency but often mismatches user habits in regions favoring the (,) for decimals, such as much of . To mitigate this, developers employ JavaScript's Intl.NumberFormat , which generates locale-aware string representations of numbers, applying the as the decimal separator in locales like French (fr-FR) while preserving the underlying value as a period-separated float for processing. Mobile operating systems enhance user experience by auto-detecting the device's locale to govern decimal separator usage in applications. On , the NSLocale class retrieves the appropriate decimal separator—such as a for locales like German (de-DE)—and applies it to input fields and displays, ensuring seamless interaction without manual configuration. Similarly, Android utilizes java.util.Locale to enforce locale-specific formatting, allowing apps in European markets to accept and render as decimals based on system settings, which reduces for users entering quantities or prices. User experience challenges in digital interfaces stem from reconciling global standards with local expectations, especially in where precise numeric entry is critical for transactions. Auto-formatting features, which dynamically insert locale-appropriate separators during typing, can interrupt the input flow and cause errors, such as unintended cursor jumps or rejected values, particularly when users switch devices or regions mid-session. Inconsistent handling exacerbates confusion in international platforms, where mismatched separators (e.g., a user entering 1,23 expecting a decimal but the system it as an ) lead to data inaccuracies and abandoned carts, underscoring the need for deferred formatting—applied only after input completion—to maintain . Recent developments in productivity apps, such as ' support for locale-based adjustments, enable handling of different decimal separators in imported datasets to enhance globalization.

Practical Applications

Real-World Examples

In the financial sector, the employs a decimal point to separate dollars from cents, as seen in the notation $3.99 for three dollars and ninety-nine cents. In contrast, uses a as the decimal separator for the , formatting the same amount as €3,99. This difference reflects broader regional conventions, where the point serves as a thousands separator in the U.S. (e.g., $1,000.00) and the fulfills that role in (e.g., €1.000,00). In scientific contexts, the scale universally adopts the decimal point, denoting neutral as 7.0 to indicate a concentration of 1.0 × 10⁻⁷ moles per liter. This standardization persists across regions due to international agreements in chemistry and physics. However, in European metric measurements, a often separates the integer and fractional parts, such as 1,609 km for one thousand six hundred nine meters. The (SI) permits both the point and as decimal separators to accommodate these variations while ensuring clarity in global scientific communication. Everyday applications highlight these conventions in routine transactions and notations. Grocery prices in the U.S. typically use a , like $2.49 for an item costing two dollars and forty-nine cents. In many European countries, the equivalent is written as €2,49, aligning with local decimal practices. For timestamps, the U.S. often employs a point in informal decimal-style writing, such as 12.30 PM to denote half past noon, whereas favors a , as in 12,30. These formats extend to schedules and logs, where misinterpretation can arise without contextual cues. Ambiguous cases emerge in international sports reporting, where decimal separators must be parsed by context to avoid errors. For instance, a recorded time of 9.58 seconds in track athletics is universally understood with a point as the decimal, but in regions using commas, a written score like 3,14 could be misread as three thousand one hundred four points instead of three point one four if viewed through a U.S. lens. Such ambiguities underscore the need for standardized digital in global events, as seen in Olympic timing systems that default to the point for precision.

Encoding in Unicode

In Unicode, the decimal separator is not assigned a single dedicated but is instead represented by existing characters, with selection determined by locale conventions as defined in the Unicode Locale Data (LDML). The (U+002E FULL STOP, .) functions as the primary decimal point in locales such as English and many Asian languages, where it separates the and fractional parts of , such as in 3.14. This character, part of the Basic Latin block, is rendered as a centered dot in mathematical contexts but adopts a baseline-aligned form for decimal use in proportional fonts. The comma (U+002C COMMA, ,), also from the Basic Latin block, serves as the decimal separator in numerous European and Latin American locales, as specified in LDML number patterns; for example, it formats 3.14 as 3,14 in French or German settings. Variant forms include the middle dot (U+00B7 MIDDLE DOT, ·) from the Latin-1 Supplement block, which is used as a raised decimal separator in scientific notation, ancient Greek texts, or languages like Catalan to avoid confusion with sentence-ending periods. Additionally, the Arabic decimal separator (U+066B ARABIC DECIMAL SEPARATOR, ٫) in the Arabic block provides a script-specific alternative, visually distinct from the full stop to align with calligraphic traditions in Arabic numerals. In bidirectional text environments, such as those mixing right-to-left (RTL) scripts like with embedded left-to-right (LTR) numbers, the Unicode Bidirectional Algorithm classifies decimal separators (including U+002E, U+002C, and U+066B) as common number separators (CS). Under rules like W4, a CS between two adjacent numbers of the same type (e.g., European or Arabic-Indic digits) inherits their directionality, ensuring the separator visually aligns with the numeric run—typically LTR for numbers within RTL text—while neutrals otherwise follow the embedding level for proper reordering. Font rendering in portable document formats like PDF relies on locale-aware processing to display these characters correctly. Systems implementing LDML, such as PDF generators, substitute the appropriate (e.g., for in fr_FR locales) based on the document's metadata or viewer settings, preventing mismatches in international distribution. This approach maintains consistency across devices, though fallback fonts may default to U+002E if locale is unavailable.

References

  1. https://docs.oracle.com/cd/E19455-01/806-0169/overview-9/index.html
  2. https://learn.microsoft.com/en-us/globalization/locale/number-formatting
  3. https://www.bipm.org/en/committees/cg/cgpm/22-2003/resolution-10
  4. https://data.europa.eu/apps/data-visualisation-guide/number-formatting
  5. https://www.iec.ch/standards-development/isoiec-directives-part-2
  6. https://www.britannica.com/science/decimal-fraction
  7. https://www.scientificamerican.com/article/the-decimal-point-is-150-years-older-than-historians-thought/
  8. https://www.iso.org/schema/isosts/v1.1/doc/n-cdf0.html
  9. https://mathworld.wolfram.com/DecimalExpansion.html
  10. https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra_(Arnold)/01%3A_The_Arithmetic_of_Numbers/1.04%3A_Decimal_Notation
  11. https://study.com/academy/lesson/decimal.html
  12. https://www.geeksforgeeks.org/maths/applications-of-decimals-in-real-life/
  13. https://old.maa.org/press/periodicals/convergence/in-these-numbers-we-use-no-fractions-a-classroom-module-on-stevins-decimal-fractions-de-thiende
  14. https://johnplaice.substack.com/p/simon-stevin-introduces-the-arithmetic
  15. https://www.bipm.org/documents/20126/41483022/si_brochure_8.pdf
  16. https://mathshistory.st-andrews.ac.uk/Biographies/Al-Uqlidisi/
  17. https://mathshistory.st-andrews.ac.uk/Miller/mathsym/fractions/
  18. https://mathshistory.st-andrews.ac.uk/Biographies/Stevin/
  19. https://www.nature.com/articles/d41586-024-00473-2
  20. https://www.sciencedirect.com/science/article/pii/S0315086024000016
  21. https://monoskop.org/images/2/21/Cajori_Florian_A_History_of_Mathematical_Notations_2_Vols.pdf
  22. https://www.bipm.org/en/committees/cg/cgpm/9-1948/resolution-7
  23. https://www.localeplanet.com/icu/decimal-symbols.html
  24. http://mathcentral.uregina.ca/QQ/database/QQ.09.99/menuge1.html
  25. https://en.wiktionary.org/wiki/radix_point
  26. https://www.ntnu.no/ntnu/old/glos/glos_nr.1_1995/stewart.html
  27. https://cdn.standards.iteh.ai/samples/3622/89963bbc1b2140c38ffb8a2ba217c456/ISO-31-1-1978.pdf
  28. https://www.gov.uk/guidance/style-guide/a-to-z
  29. https://www.noslangues-ourlanguages.gc.ca/en/writing-tips-plus/numbers-decimal-fractions
  30. https://finance.cornell.edu/treasurer/cash-management/processinginternational/intl-currency
  31. https://www.themathdoctors.org/decimals-commas-thousands-and-lakhs/
  32. https://byjus.com/maths/indian-place-value-chart/
  33. https://www.languageediting.com/number-formatting-europe-vs-us/
  34. https://www.smartick.com/blog/other-contents/curiosities/decimal-separators/
  35. https://mathworld.wolfram.com/DecimalPoint.html
  36. https://www.nist.gov/news-events/news/2006/11/decimals-score-point-international-standards
  37. https://help-center.helioscope.com/hc/en-us/articles/8537789483795-International-CSV-Exports-Format-Change
  38. https://stackoverflow.com/questions/15282791/in-binary-notation-what-is-the-meaning-of-the-digits-after-the-radix-point
  39. https://electronics.stackexchange.com/questions/131331/decimal-binary-hex-base7-conversions-with-radix-points
  40. https://www.unicode.org/L2/L2017/17324-decimal-full-stop.pdf
  41. https://www.thatsmandarin.com/chinese-language/numbers-decimals-fractions-percentage-in-chinese/
  42. https://academia.stackexchange.com/questions/117982/central-dot-as-decimal-point-in-top-journal
  43. https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf
  44. https://www.iso.org/standard/30669.html
  45. https://www.iso.org/standard/75812.html
  46. https://www.iso.org/standard/80985.html
  47. https://www.un.org/dgacm/en/content/editorial-manual/numbers-dates-time
  48. https://unesdoc.unesco.org/ark:/48223/pf0000116005
  49. https://www.nist.gov/pml/owm/metric-si-prefixes
  50. https://language-boutique.com/lost-in-translation-full-reader/writing-numbers-points-or-commas.html
  51. https://jref.com/articles/decimals-and-fractions-in-japanese.351/
  52. https://elisabethirgens.github.io/notes/2020/03/decimal-and-thousands-separators/
  53. https://peps.python.org/pep-0378/
  54. https://ux.stackexchange.com/questions/20353/is-a-number-easier-to-read-with-the-thousand-separator
  55. https://www.iso.org/sites/directives/current/part2/index.xhtml
  56. https://www.calcsimpler.com/units-and-measures/iso-80000-1-general-principles
  57. https://haacked.com/archive/2020/05/17/french-thousand-separator-mystery/
  58. https://helpcenter.spinifexit.com/hc/en-us/articles/18889737257881-Switzerland-Number-Format
  59. https://physics.nist.gov/cuu/Units/checklist.html
  60. https://support.microsoft.com/en-us/office/change-the-character-used-to-separate-thousands-or-decimals-c093b545-71cb-4903-b205-aebb9837bd1e
  61. https://www.allaboutcircuits.com/textbook/digital/chpt-2/bit-grouping/
  62. https://datatracker.ietf.org/doc/html/rfc4291
  63. https://byjus.com/maths/numeral-system/
  64. https://www.six-group.com/en/blog/ticker-symbols.html
  65. https://support.microsoft.com/en-us/office/control-data-entry-formats-with-input-masks-e125997a-7791-49e5-8672-4a47832de8da
  66. https://peps.python.org/pep-0515/
  67. https://www.si.edu/spotlight/slide-rules/linear-slide-rules
  68. https://www.oughtred.org/jos/articles/V7.1_Chamberlain_Decimals.pdf
  69. https://americanhistory.si.edu/collections/object-groups/handheld-electronic-calculators/introduction
  70. http://www.vintagecalculators.com/html/texas_instruments_2500.html
  71. http://www.vintagecalculators.com/html/history_of_electronic_calculators.html
  72. https://ia600401.us.archive.org/23/items/enf-ascii-1968-1970/Image070917151315.pdf
  73. https://www.govinfo.gov/content/pkg/GOVPUB-C13-94615700fab4eb48cd4ef70134b637be/pdf/GOVPUB-C13-94615700fab4eb48cd4ef70134b637be.pdf
  74. https://docs.oracle.com/javase/specs/jls/se8/html/jls-3.html
  75. https://docs.python.org/3/library/locale.html
  76. https://unicode-org.github.io/icu-docs/apidoc/released/icu4c/classDecimalFormat.html
  77. https://ieeexplore.ieee.org/document/8766229
  78. https://learn.microsoft.com/en-us/answers/questions/4377252/%28article%29-power-query-how-to-import-a-csv-file-tha
  79. https://html.spec.whatwg.org/multipage/input.html
  80. https://developer.mozilla.org/en-US/docs/Web/HTML/Reference/Elements/input/number
  81. https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Intl/NumberFormat
  82. https://developer.apple.com/documentation/foundation/nslocale/decimalseparator
  83. https://ux.stackexchange.com/questions/38870/is-constantly-updating-the-formatting-of-a-numeric-input-box-a-good-idea
  84. https://www.shopery.com/insights/the-importance-of-number-formats-in-saas-platforms
  85. https://support.google.com/docs/answer/58515?hl=en
  86. https://fastspring.com/blog/how-to-format-30-currencies-from-countries-all-over-the-world/
  87. https://chem.libretexts.org/Courses/Saint_Marys_College_Notre_Dame_IN/CHEM_118_%28Under_Construction%29/CHEM_118_Textbook/09%253A_Acids_Bases_and_Buffers/9.09%253A_The_pH_Scale
  88. https://physics.nist.gov/cuu/pdf/sp811.pdf
  89. https://www.star-ts.com/translation-faq/how-world-monetary-values-are-displayed/
  90. https://www.ricksteves.com/travel-tips/trip-planning/european-numbers
  91. https://www.theguardian.com/sport/2012/aug/12/olympic-records-time-numbers-mathematics
  92. https://www.unicode.org/charts/nameslist/n_0000.html
  93. https://unicode.org/reports/tr35/tr35-numbers.html
  94. https://www.unicode.org/reports/tr9/
  95. https://www.unicode.org/reports/tr9/#W4
Add your contribution
Related Hubs
User Avatar
No comments yet.