- Decimal separator
In a positional

numeral system , the**decimal separator**is asymbol used to mark the boundary between the integral and the fractional parts of adecimal numeral . When used in context ofArabic 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 system s may be referred to as aradix point . In a binary system, it is sometimes referred to asbinary 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 theunits digit was used to separate the integral part of a number from its fractional part, a tradition derived from the decimal system used inIndian mathematics . [*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*] Its regular usage and classification can be attributed to the Iranianmathematician Al-Khwarizmi . Later, a separator (ˌ) (a short, roughly vertical, ink stroke) between the units and tenths position became the norm. When this character wastypeset , it was convenient to use the existing comma (,) or period (.) instead.In

France , the period was already in use in printing to makeRoman numerals more readable, so the comma was chosen. Many other countries also chose to use the comma to mark the decimal units position. [*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."*] 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 aninterpunct , was preferred for the decimal separator in printing technologies that could accommodate it. [*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*] 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, theSI rejected this use of the middle dot as the decimal separator. However, the use of the period as decimal separator was not banned. Britishaviation magazines thus switched to the US form in the late twentieth century.When

South Africa adopted themetric system , it adopted the comma as its decimal separator. The auxiliary languageInterlingua has used the comma as its decimal separator since the publication of the in 1951. [*[*] The*http://members.optus.net/~ado_hall/interlingua/gi/parts_of_speech/numerals.html Grammar of Interlingua: Parts of Speech - Numerals*]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. [*Perlis, Alan, "The American Side of the Development of ALGOL", ACM SIGPLAN Notices, August 1978.*]**Digit grouping**Numbers with many digits before or afterFact|date=August 2007 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 [*http://www.nist.gov/public_affairs/techbeat/tb2006_1122.htm#decimal*] ; 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).Fact|date=June 2008 This does not apply in mathematical and other technical contexts.

The International Union of Pure and Applied Chemistry (IUPAC) suggests to never use a comma or a point as thousands separator:"For numbers with many digits, the digits may be separated in groups of three, counting from the decimal sign toward the left and the right. The groups should be separated by a thin space (half space), and never by a comma or a point, or by any other means." [

*http://old.iupac.org/reports/provisional/guidelines.html*]**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 ofLatin Europe as well as FrenchCanada : 1 234 567,89 (InSpain , in handwriting it is also common to use an upper comma: 123.456'98)

* InGermany ,Belgium ,Denmark ,Italy ,Romania ,Sweden and much of Europe: 1 234 567,89 or 1**.**234**.**567,89 (inhandwriting , 1**˙**234**˙**567,89 is also seen)

* In theNetherlands : 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

* InSwitzerland : 1'234'567,89; for thousand separator an apostrophe is used.

* InAustralia , English Canada,Japan ,Korea (both),Malaysia ,Singapore , thePhilippines , theUnited Kingdom , and theUnited States : 1,234,567**.**89 or 1,234,567**·**89; the latter is more commonly found in older, and especiallyhandwritten , documents; many British and Canadian schools now teach theSI style with a dot separator, which has become official inAustralia .

*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 10^{8}). Japan is similar.* In

India , due to a numeral system using "lakh s" ("lac s") (1,00,000 equal to 100 000) and "crore s" (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 calculator s, which use the decimal point. Most computeroperating 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**Countries where a dot is used to mark the radix point include::

Australia ,Brunei ,Botswana ,Canada (English-speaking),Hong Kong ,India , Ireland,Israel ,Japan ,Kenya ,Korea (both North and South),Malaysia ,Mexico ,New Zealand ,Nigeria ,Pakistan ,People's Republic of China ,Philippines ,Singapore ,Sri Lanka ,Switzerland (for currencies),Taiwan ,Tanzania ,Thailand ,Uganda ,United Kingdom ,United States (includinginsular area s),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 (officiallyFact|date=July 2008, but dot point is commonly used in business),Slovenia ,Spain ,Sweden ,Switzerland ,Turkey ,Ukraine ,Uruguay ,Venezuela ,Vietnam .**Other numeral systems**In the

Arab world , whereEastern 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 inUnicode . 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

sequence s 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. [*cite web|url=http://unicode.org/mail-arch/unicode-ml/Archives-Old/UML024/1289.html|title=Persian decimal separator|last=Pournader|first=Roozbeh|date=2000-10-15|work=Unicode Mail List Archive|publisher=Unicode Consortium|accessdate=2008-06-21*] [*cite web*] [

url=http://www.fazel.de/dastur/EN/2-1-05-001-1-3_decimal_numeral.html

title=The Decimal Numeral

work=Academic Grammar of New Persian

accessdate=2006-06-19*[*]*http://web.archive.org/web/20070711041230/http://www.fazel.de/dastur/EN/2-1-05-001-1-3_decimal_numeral.html Descriptive Grammar of New Persian (archived)*]**ee also***

Algorism **References**

*Wikimedia Foundation.
2010.*

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