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Decimal separator

A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form (e.g., "." in 12.45). Different countries officially designate different symbols for use as the separator. The choice of symbol also affects the choice of symbol for the thousands separator used in digit grouping.

For decimal separator use in Wikipedia articles, see Wikipedia:Manual of Style (dates and numbers) § Decimal points.

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]


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.

In Albania, Belgium (French), Estonia, Finland, 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)

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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 , 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.[62]

handwriting

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[64] for "eine Milliarde 234 Millionen ...", but this is never seen in modern days and requires explanation to a contemporary German reader.

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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 -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 —.

SI

In Ireland, Israel, Japan, (both), Malaysia, 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.

Korea

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.

style: 1234567.89 or 1234567,89 (in their own publications, the dot "." is used in the English version, and the comma "," in the official French version).

SI

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, or characters are frequently used as separators: 1億2345万6789 / 1億2345萬6789. Commas are used when grouping by thousands.

kanji

In , 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), a 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.

India

In , the currency sometimes used the colon as decimal separator (1 234 567:89).

Sweden

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

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 (˙, ˙)

Used with Western Arabic numerals (0123456789):


Used with Eastern Arabic numerals (٠١٢٣٤٥٦٧٨٩):


Used with keyboards: