Decimal separator

A decimal separator is a symbol that separates the integer part from the fractional part of a number written in decimal form. Different countries officially designate different symbols for use as the separator. The choice of symbol can also affect the choice of symbol for the thousands separator used in digit grouping.
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 and comma respectively, when it is used as a decimal separator; these are the usual terms used in English, with the aforementioned generic terms reserved for abstract usage.
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. In some specialized contexts, the word decimal is instead used for this purpose. 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

Hellenistic–Renaissance eras

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 995. A similar notation remains in common use as an underbar to superscript digits, especially for monetary values without a decimal separator, as in 99. Later, a "separatrix" between the units and tenths position became the norm among Arab mathematicians, while an L-shaped or vertical bar served as the separatrix in England. When this character was typeset, it was convenient to use the existing comma or full stop 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. The practice is ultimately derived from the decimal Hindu–Arabic numeral system used in Indian mathematics, and popularized by the Persian mathematician Al-Khwarizmi, 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, 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.
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.
Tables of logarithms prepared by John Napier in 1614 and 1619 used the period 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.
Many other countries, such as Italy, also chose to use the comma to mark the decimal units position. 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 some countries, a raised dot or dash may be used for grouping or decimal separator; this is particularly common in handwriting.

English-speaking countries

In the United States, the full stop or period is used as the standard decimal separator.
In the nations of the British Empire, the full stop could be used in typewritten material and its use was not banned, although the interpunct was preferred as a decimal separator, in printing technologies that could accommodate it, e.g. 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.
When South Africa adopted the metric system, it adopted the comma as its decimal separator, although a number of house styles, including some English-language newspapers such as The Sunday Times, continue to use the full stop.
Previously, signs along California roads expressed distances in decimal numbers with the decimal part in superscript, as in 3⁷, meaning 3.7. Though California has since transitioned to mixed numbers with common fractions, the older style remains on postmile markers and bridge inventory markers.

Constructed languages

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.
Esperanto also uses the comma as its official decimal separator, whilst thousands are usually separated by non-breaking spaces. It is possible to separate thousands by a full stop, though this is not as common.
Ido's Kompleta Gramatiko Detaloza di la Linguo Internaciona Ido officially states that commas are used for the decimal separator whilst full stops are used to separate thousands, millions, etc. So the number 12,345,678.90123, for instance, would be written 12.345.678,90123 in Ido.
The 1931 grammar of Volapük uses the comma as its decimal separator but, somewhat unusually, the middle dot as its thousands separator.
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. ALGOL ended up allowing different decimal separators, but most computer languages and standard data formats specify a dot. C++ and a few others permit a quote as a thousands separator, while others like Python and Julia only allow '_' as such a separator

Radix point

In mathematics and computing, a radix point or radix character is a symbol used in the display of numbers to separate the integer part of the value from its fractional part. In English and many other languages, the integer part is at the left of the radix point, and the fraction part at the right of it.
A radix point is most often used in decimal notation, when it is more commonly called the decimal point. In English-speaking countries, the decimal point is usually a small dot placed either on the baseline, or halfway between the baseline and the top of the digits
In many other countries, the radix point is a comma placed on the baseline.
These conventions are generally used both in machine displays and in handwriting. It is important to know which notation is being used when working in different software programs. The respective ISO 31-0 standard defines both the comma and the small dot as decimal markers, but does not explicitly define universal radix marks for bases other than 10.
Fractional numbers are rarely displayed in other number bases, but, when they are, a radix character may be used for the same purpose. When used with the binary representation, it may be called "binary point".

Current international standards

The 22nd General Conference on Weights and Measures declared in 2003, "The symbol for the decimal marker shall be either the point on the line or the comma on the line." It further reaffirmed,
That is, "" is preferred over "1,000,000,000" or "1.000.000.000". This use has therefore been recommended by technical organizations, such as the United States's National Institute of Standards and Technology.
Past versions of ISO 8601, but not the 2019 revision, also stipulated normative notation based on SI conventions, adding that the comma is preferred over the full stop.
ISO 80000-1 stipulates, "The decimal sign is either a comma or a point on the line." The standard does not stipulate any preference, observing that usage will depend on customary usage in the language concerned, but adds a note that as per ISO/IEC directives, all ISO standards should use the comma as the decimal marker.

Digit grouping

For ease of reading, numbers with many digits may be divided into groups using a delimiter, such as comma, dot, half-space or thin space, space, underscore, 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 telling at a glance rather than counting.
The use of thin spaces as separators instead of dots or commas, has been official policy of the International Bureau of Weights and Measures since 1948,
as well as of the International Union of Pure and Applied Chemistry, the American Medical Association's widely followed AMA Manual of Style, and the UK Metrication Board, among others.
The groups created by the delimiters tend to follow the usages of local languages, which vary. In European languages, large numbers are read in groups of thousands, and the delimiter may be called a "thousands separator". In East Asian cultures, particularly China, Japan, and Korea, large numbers are read in groups of myriads, but the delimiter often separates the digits into groups of three.
The Indian numbering system is more complex: It groups the rightmost three digits together and then groups digits in sets of two. For example, one trillion would be written "10,00,00,00,00,000" or "".
The convention for digit group separators historically varied among countries, but usually sought 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. 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, as well as by the BIPM and IUPAC. These groups have also begun advocating the use of a "thin space" in "groups of three".
Within the United States, the American Medical Association's widely followed AMA Manual of Style also calls for a thin space. In programming languages and online encoding environments a thin space is not practical or available. Often, either underscores and regular word spaces, or no delimiters at all are used instead.