Decimal separator

The decimal separator is a symbol used to mark the boundary between the integral and the fractional parts of a decimal numeral. Terms implying the symbol used are decimal point and decimal comma.

The decimal separator is mathematically a radix point.

The choice of symbol for the decimal separator affects the choice of symbol for the thousands separator. 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 (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 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. The constructed language Esperanto also uses the comma as its official decimal separator.

In the Arab world and Iran, where Arabic digits are used for writing numbers, a different character called momayyez — which is written like a forward slash — is used to separate the integer and fractional parts of numbers. 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 small difference between the "comma" character used in sentences and the comma-like character used to separate sequences of three digits.[1]

The separator in non-decimal numeral systems may be referred to as a radix point.

In 1958, disputes between European and American delegates over the correct representation of the decimal separator nearly stalled the development of the ALGOL language. ^[4]

Thousands separator

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 [2]; 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). This does not apply in mathematical and other technical contexts.

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 France, Finland, Hungary, Poland, Czech Republic, Slovakia and much of Latin Europe as well as French Canada: 1 234 567,89
In Germany, the Netherlands, 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 Switzerland (mainly German-speaking Switzerland): 1'234'567.89
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 (a comma may be used, but in their own publications only the dot is used)
In China, the comma is sometimes used to separate blocks of four digits: 123,4567.89, since in Chinese, the names for large numbers 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 (100,000) and crores (10,000,000), an asymmetric distribution of comma separators is commonly used, for example, 30 million (3 crores) would be written as 3,00,00,000, with commas at the thousand, lakh, and crore levels.

In countries with a decimal comma, the decimal point is also common as the "international" notation and under the influence of e.g. electronic calculators using 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.

Dot countries

Decimal Separators: Dot — Blue, Comma — Green, Momayyez — 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, Peru, Philippines, Singapore, Sri Lanka, Switzerland, Taiwan, Thailand, United Kingdom, United States (including insular areas), Zimbabwe.

Comma countries

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, Cuba, Chile, Colombia, Cyprus, Czech Republic, Denmark, Dominican Republic, Ecuador, El Salvador, Estonia, Faroes, Finland, France, Germany, Greece, Greenland, Guatemala, Honduras, Hong Kong, Hungary, Indonesia, Iceland, Italy, Kazakhstan, Latvia, Lithuania, Luxembourg (uses both separators officially), Macedonia, Moldova, Netherlands, Norway, Nicaragua, Panama, Paraguay, Poland, Portugal, Romania, Russia, Serbia, Slovakia, South Africa (officially, but dot point is commonly used in business), Slovenia, Spain, Sweden, Turkey, Ukraine, Uruguay, Venezuela, Vietnam/

Momayyez countries

Bahrain, Iran, Iraq, Kuwait, Oman, Qatar, Saudi Arabia, Syria, UAE

References

^ Reimer, L. and Reimer, W. Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians, Vol. 2. 1995. pp.22-22. Parsippany, NJ: Pearson Education, Inc. as Dale Seymor Publications. ISBN 0-86651-823-1
^ Enciclopedia Universal Santillana, 1996 by SANTILLANA S.A., Barcelona, Spain. ISBN 84-294-5129-3. Comma, def.2: "coma: MAT. Signo utilizado en los números no enteros para separar la parte entera de la parte decimal o fraccionaria; p.ej., 2,123."
^ Reimer, L. and Reimer, W. Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians, Vol. 1. 1990 p.41. Parsippany, NJ: Pearson Education, Inc. as Dale Seymor Publications. ISBN 0-86651-509-7
^ Perlis, Alan, The American Side of the Development of ALGOL, ACM SIGPLAN Notices, August 1978.

[1] Reimer, L. and Reimer, W. Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians, Vol. 2. 1995. pp.22-22. Parsippany, NJ: Pearson Education, Inc. as Dale Seymor Publications. ISBN 0-86651-823-1

[2] Enciclopedia Universal Santillana, 1996 by SANTILLANA S.A., Barcelona, Spain. ISBN 84-294-5129-3. Comma, def.2: "coma: MAT. Signo utilizado en los números no enteros para separar la parte entera de la parte decimal o fraccionaria; p.ej., 2,123."

[3] Reimer, L. and Reimer, W. Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians, Vol. 1. 1990 p.41. Parsippany, NJ: Pearson Education, Inc. as Dale Seymor Publications. ISBN 0-86651-509-7

[4] Perlis, Alan, The American Side of the Development of ALGOL, ACM SIGPLAN Notices, August 1978.

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