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In a positional numeral system, the decimal separator is a symbol used to mark the boundary between the integral and the fractional parts of a decimal numeral. When used in context of Arabic numerals, terms implying the symbol used are decimal point and decimal comma.

The decimal separator is mathematically a radix point. The English term "decimal" is limited to base ten, but the separator in non-decimal numeral systems may be referred to as a radix point. In a binary system, it is sometimes referred to as binary point.

The choice of symbol for the decimal separator affects the choice of symbol for the thousands separator used in digit grouping. Consequently the latter is treated in this article as well.

History

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, a tradition derived from the decimal system used in Indian mathematics^[1]. Its regular usage and classification can be attributed to the Iranian mathematician Al-Khwarizmi. Later, a separator (ˌ) (a short, roughly vertical, ink stroke) between the units and tenths position became the norm. When this character was typeset, it was convenient to use the existing comma (,) or period (.) instead.

In France, the period was already in use in printing to make Roman numerals more readable, so the comma was chosen. Many other countries also chose to use the comma to mark the decimal units position^[2]. It has been made standard by the ISO for international blueprints. However, English-speaking countries took the comma to separate sequences of three digits.

In the United States, the period (.), which is called a "stop" or "full stop" in some other countries, was used as the standard decimal separator. In the nations of the British Empire, although the period could be used in typewritten material, the point (middle dot: ·), which can also be called an interpunct, was preferred for the decimal separator in printing technologies that could accommodate it^[3]. This had the advantage of reducing confusion in the countries that used the period to separate groups of digits and it was generally clearer in handwriting (particularly when writing on a dotted baseline as on many forms). However, as the middle dot was already in common use in the mathematics world to indicate multiplication, the SI rejected this use of the middle dot as the decimal separator. However, the use of the period as decimal separator was not banned. British aviation magazines thus switched to the US form in the late twentieth century.

When South Africa adopted the metric system, it adopted the comma as its decimal separator. The auxiliary language Interlingua has used the comma as its decimal separator since the publication of the Interlingua Grammar in 1951^[4]. The constructed language Esperanto also uses the comma as its official decimal separator.

In 1958, disputes between European and American delegates over the correct representation of the decimal separator nearly stalled the development of the ALGOL language^[5].

Digit grouping

Numbers with many digits before or after^{citation needed} the decimal separator may be divided into groups of three, starting from the decimal separator in both directions. The symbol for this is called the thousands separator or, more generally (see India and China below), digit group separator. If the decimal separator is a point, the thousands separator is often a comma or a space. The latter is recommended in the SI/ISO 31-0[1]; when a space is used, it is often used after the decimal separator too, thus "1 234.567 89". If the decimal separator is a comma, the thousands separator is often a point or a space. Notations like "12,345", "12.345", "12,345.678", and "12.345,678" are ambiguous if the notational system is not known.

Making groups of three digits also emphasizes that there is a base 1000 of the numeral system that is being used (see decimal superbase).

The house manuals of style for many publishing organizations state that thousands separators should not be used in normal text for numbers from 1000 to 9999 inclusive where no decimal fractional part is shown (in other words, for four-digit whole numbers).^{citation needed} This does not apply in mathematical and other technical contexts.

Arabic numeral system

Examples of use

The following examples show the decimal separator and the thousands separator; the lists are ordered chronologically, by when each country adopted the use:

• In Croatia, Estonia, France, Finland, Hungary, Poland, Czech Republic, Slovakia and much of Latin Europe as well as French Canada: 1 234 567,89
• In Germany, Belgium, Denmark, Italy, Romania, Sweden and much of Europe: 1 234 567,89 or 1.234.567,89 (in handwriting you may also come across 1˙234˙567,89)
• In the Netherlands: for currencies the thousands separator is a dot, e.g. EUR 1.234.567,89, but for other numbers a (narrow) space is used, e.g. 1 234 567,89
• In Switzerland : 1'234'567,89, but the dot is generally used as decimal seperator for currencies : CHF 1'234.55
• In Australia, English Canada, Japan, Korea (both), Malaysia, Singapore, the United Kingdom, and the United States: 1,234,567.89 or 1,234,567·89; the latter is more commonly found in older, and especially handwritten, documents; many British and Canadian schools now teach the SI style with a dot separator, which has become official in Australia.
• 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 French version).
• In Chinese, 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. However, grouping can also be done every four digits: 123,4567.89, since names for large numbers in Chinese are based on powers of 10,000 (e.g. the next new word is for 10⁸). Japan is similar.

• In India, due to a numeral system using lakhs (lacs) (1,00,000 equal to 100 000) and crores (1,00,00,000 equal to 10 000 000), comma is used at levels of thousand, lakh and crore, for example, 10 million (1 crore) would be written as 1,00,00,000. This is repeated at thousand crore, one lakh crore and a crore crore (1,00,00,000,00,00,000). Note that the pattern of comma is groups of 3,2,2 again 3,2,2 from right side.

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 and programs that have been carefully internationalised will follow this, but some programs ignore it and a few are even broken by it.

Countries using Arabic numerals with decimal point

Decimal Separators:
Dot — Blue
Comma — Green
Non-Arabic Numerals — Red
Unknown — Grey

Countries where a dot is used to mark the radix point include:

Australia, Brunei, Botswana, Canada (English-speaking), Hong Kong, India, Ireland, Israel, Japan, Korea (both North and South), Malaysia, Mexico, New Zealand, Nigeria, Pakistan, People's Republic of China, Philippines, Singapore, Sri Lanka, Switzerland (for currencies), Taiwan, Thailand, United Kingdom, United States (including insular areas), Zimbabwe.

Countries using Arabic numerals with decimal comma

Countries where a comma is used to mark the radix point include:

Albania, Andorra, Argentina, Austria, Azerbaijan, Belarus, Belgium, Bolivia, Bosnia and Herzegovina, Brazil, Bulgaria, Cameroon, Canada (French-speaking), Costa Rica, Croatia (comma used officially, but both forms are in use elsewhere), Chile, Colombia, Cuba, Cyprus, Czech Republic, Denmark, Dominican Republic, Ecuador, El Salvador, Estonia, Faroes, Finland, France, Germany, Greece, Greenland, Guatemala, Honduras, Hungary, Indonesia, Iceland, Italy, Kazakhstan, Latvia, Lithuania, Luxembourg (uses both separators officially), Macedonia, Moldova, Netherlands, Norway, Nicaragua, Panama, Paraguay, Peru, Poland, Portugal, Romania, Russia, Serbia, Slovakia, South Africa (officially^{citation needed}, but dot point is commonly used in business), Slovenia, Spain, Sweden, Switzerland, Turkey, Ukraine, Uruguay, Venezuela, Vietnam.

Other numeral systems

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 Arabic Decimal Separator 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 "comma" character used in sentences and the Momayyez (٫) used to separate sequences of three digits. To separate sequences of three digits, a comma or blank space may be used; however this is not a standard. In Persian, there is a little difference between the "comma" character used in sentences, and the comma-like character used to separate sequences of three digits.^[6][7][8]

See also

• Algorism

References