Decimal separator

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, e.g. 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, e.g. 99⁹⁵. Later, a "separatrix" (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.[7] 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.[8] The practice is ultimately derived from the decimal Hindu-Arabic numeral system used in Indian mathematics[9] and popularized by the Persian mathematician Al-Khwarizmi,[10] 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.[11] 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.[12] Many other countries, such as Italy, also chose to use the comma to mark the decimal units position.[12] It has been made standard by the ISO for international blueprints.[13] However, English-speaking countries took the comma to separate sequences of three digits. In some countries, a raised dot or dash (upper comma) may be used for grouping or decimal separator; this is particularly common in handwriting.

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

The interpunct (·) used as a decimal separator in a British print from 1839[14]

In the nations of the British Empire, although the full stop could be used in typewritten material and its use was not banned, the interpunct (also known as the decimal point, point, or mid dot) was preferred for the decimal separator in printing technologies that could accommodate it, e.g. 99·95.[15] 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.[16]

When South Africa adopted the metric system, it adopted the comma as its decimal separator,[17] although a number of house styles, including some English-language newspapers such as The Sunday Times, continue to use the full stop.

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.[18] Esperanto also uses the comma as its official decimal separator, while thousands are separated by non-breaking spaces: 12 345 678,9. 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 while 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 by Arie de Jong uses the comma as its decimal separator, and (somewhat unusually) uses the middle dot as the thousands separator (12·345·678,90123).[19]

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.[20] 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.

California milepost marker at mile 144.44

Previously, signs along California roads expressed distances in decimal numbers with the decimal part in superscript, as in 3⁷, meaning 3.7.[21] Though California has since transitioned to mixed numbers with common fractions, the older style remains on postmile markers and bridge inventory markers.

The 22nd General Conference on Weights and Measures declared in 2003 that "the symbol for the decimal marker shall be either the point on the line or the comma on the line". It further reaffirmed that "numbers may be divided in groups of three in order to facilitate reading; neither dots nor commas are ever inserted in the spaces between groups"[22] (e.g. 1000000000). This usage has therefore been recommended by technical organizations, such as the United States' National Institute of Standards and Technology.[23]

ISO-8601 also stipulates normative notation based on SI conventions, adding that the comma is preferred over the full stop. [24]

For ease of reading, numbers with many digits may be divided into groups using a delimiter,[25] such as comma "," or dot ".", half-space " ", space " ", underbar "_" (as in maritime "21_450") 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 subitizing (telling at a glance) rather than counting – contrast 100000000 with 100000000 for one hundred million.

Since 2003,[26] the use of spaces as separators (for example: 20000 and 1000000 for "twenty thousand" and "one million") has been officially endorsed by SI/ISO 31-0 standard,[27] as well as by the International Bureau of Weights and Measures and the International Union of Pure and Applied Chemistry (IUPAC),[28][29] the American Medical Association's widely followed AMA Manual of Style, and the Metrication Board, among others.

The groups created by the delimiters tend to follow the use of the local language, which varies. In European languages, large numbers are read in groups of thousands and the delimiter (which occurs every three digits when it is 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 commonly separates every three digits. The Indian numbering system is somewhat more complex: it groups the rightmost three digits together (till the hundreds place) and thereafter groups by sets of two digits. One trillion would thus be written as 10,00,00,00,00,000 or 10 kharab.[30]

The convention for digit group separators historically varied among countries, but usually seeking to distinguish the delimiter from the decimal separator. Traditionally, English-speaking countries employed commas as the delimiter – 10,000 – and other European countries employed periods or spaces: 10.000 or 10000. 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,[27] as well as by the International Bureau of Weights and Measures and the International Union of Pure and Applied Chemistry, which have also begun advocating the use of a "thin space" in "groups of three".[28][29] Within the United States, the American Medical Association's widely followed AMA Manual of Style also calls for a thin space.[25] In some online encoding environments (for example, ASCII-only) a thin space is not practical or available, in which case a regular word space or no delimiter are the alternatives.

In countries with a decimal comma, the decimal point is also common as the "international" notation 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.

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 (٫) (in hex U+066B) in Unicode. An Arabic thousands separator (٬) also exists.

In Persian, the decimal separator is called momayyez, which is written like a forward slash—there is a small difference between the upside-down (Persian) comma character used in sentences and the Latin comma (٫) (in hex U+066B) used to separate sequences of three digits. To separate sequences of three digits, a Latin comma or blank space may be used; however this is not a standard.[40][41][42]

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

The following examples show the decimal separator and the thousands separator in various countries that use the Arabic numeral system.

• In Albania, Belgium (French), Estonia, Finland,[46] France, Hungary, Poland, Slovakia and much of Latin Europe as well as French Canada: 1234567,89 (In Spain, in handwriting it is also common to use an upper comma: 1.234.567'89)
• 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. 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, the points thousands separator is used, and is preferred for currency amounts, but the space is recommended by some style guides, mostly in technical writing.[47]
• 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 comma and point, e.g. 1.234,567.890,12[48][49] for "eine Milliarde 234 Millionen ...", but this is never seen in modern days and requires explanation to a contemporary German reader.
• Switzerland: There are two cases: An apostrophe as a thousands separator along with a dot "." as the decimal separator are used for currency values (for example: 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 variety for non-currency values: 1'234'567,89 — though this usage is officially discouraged.
• In Ireland, Israel, Japan, Korea (both), Malaysia, New Zealand, the Philippines, Singapore, Taiwan, Thailand, the United Kingdom, and the United States: 1,234,567.89 or 1,234,567·89; the latter is generally found only in older, and especially handwritten documents. Australia used this style up until the 1970s; now it uses the SI style.[50][51]
• English Canada: There are two cases: The preferred method for currency values is $10,000.00 —while for numeric values, it is 1234567.89; however, commas are also sometimes used, although no longer taught in school or used in official publications.
• SI style: 1 234 567.89 or 1 234 567,89 (in their own publications, the dot "." is used in the English version, and the comma "," in the official French version).
• In China, comma and space are used to mark digit groups, because dot is used as decimal separator. There is no universal convention on digit grouping, so both thousands grouping and no digit grouping can be found. Japan and Taiwan are similar; although when grouping by myriads, kanji or characters are frequently used as separators: 1亿2345万6789 / 1億2345萬6789. Commas are used when grouping by thousands.
• In India, due to a numeral system using lakhs (lacs) (1,23,456 equal to 123,456) and crores (1,23,45,678 equal to 12,345,678), comma is used at levels of thousand; lakh and crore, for example, 10 million (1 crore) would be written as 1,00,00,000. In Pakistan, there is a greater tendency to use the standard western system, while using the Indian numbering system when conducting business in Urdu.

Used with Western Arabic numerals (0123456789):

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

Used with Eastern Arabic numerals (٠١٢٣٤٥٦٧٨٩):

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

Used with keyboards:

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

• Algorism
• Decimal place
• Decimal representation
• International System of Units
• RKM code
• Version numbering
• Cifrão