| Numeral systems by culture | |
|---|---|
| Hindu-Arabic numerals | |
| Western Arabic (Hindu numerals) Eastern Arabic Indian family Tamil |
Burmese Khmer Lao Mongolian Thai |
| East Asian numerals | |
| Chinese Japanese Suzhou |
Korean Vietnamese Counting rods |
| Alphabetic numerals | |
| Abjad Armenian Āryabhaṭa Cyrillic |
Ge'ez Greek Georgian Hebrew |
| Other systems | |
| Aegean Attic Babylonian Brahmi Egyptian Etruscan Inuit |
Kharosthi Mayan Quipu Roman Sumerian Urnfield |
| List of numeral system topics | |
| Positional systems by base | |
| Decimal (10) | |
| 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 20, 24, 30, 36, 60, 64 | |
| Non-positional system | |
| Unary numeral system (Base 1) | |
| List of numeral systems | |
Different symbols have been and are used for the decimal mark. The choice of symbol for the decimal mark affects the choice of symbol for the thousands separator used in digit grouping. Consequently the latter is treated in this article as well.
The decimal mark 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.
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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 Persian mathematician Al-Khwarizmi.[2] It remains in common use as an underbar to superscript digits, especially for monetary pricing values. e.g. 9995 without a decimal point.
Later, a separator (ˌ) (a short, roughly vertical, ink stroke) between the units and tenths position became the norm among Islamic mathematicians. 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, such as Italy.[3] 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 other countries, was used as the standard decimal mark. In the nations of the British Empire, although the period could be used in typewritten material, the point (mid dot: ·), which can also be called an interpunct (often referred to as the decimal point) was preferred for the decimal mark in printing technologies that could accommodate it.[4] 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 mid dot was already in common use in the mathematics world to indicate multiplication, the SI rejected its use as the decimal mark. However, the use of the period as decimal mark 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 mark [5], although a number of house styles, including leading newspapers like The Star and The Sunday Times continue to use the decimal point. The auxiliary language Interlingua has used the comma as its decimal mark since the publication of the Interlingua Grammar in 1951.[6] Another international auxiliary language, Esperanto, also uses the comma as its official decimal mark.
In 1958, disputes between European and American delegates over the correct representation of the decimal mark nearly stalled the development of the ALGOL computer programming language.[7] ALGOL ended up allowing different decimal marks, but most computer languages and standard data formats (e.g. C, Java, Fortran, Cascading Style Sheets (CSS)) specify a dot.
The 22nd General Conference on Weights and Measures declared in 2003 that "the symbol for the decimal marker shall be either the point on the line or the comma on the line". It further reaffirmed that "numbers may be divided in groups of three in order to facilitate reading; neither dots nor commas are ever inserted in the spaces between groups".[8]
For ease of reading, numbers with many digits before or after the decimal mark may be divided into groups using a delimiter, with the counting of groups starting from the decimal mark in both directions.[9] This delimiter is usually called a thousands separator, because the digits are usually in groups of three, that is, thousands. The most general name for this delimiter is digit group separator, because thousands are not always the relevant group. For example, in various countries (e.g., China, India, and Japan), there have been traditional conventions of grouping by 2 or 4 digits. These conventions are still observed in some contexts, although the 3-digit group convention is also well known and often used. Making groups of three digits also emphasizes that there is a base 1000 of the numeral system that is being used, which is not always a given (for example, in computer science).
As with the decimal mark, there have been several common conventions for which character to use for the digit group separator. If the decimal mark is a point, the digit group separator is often a comma or a space. If the decimal mark is a comma, the digit group separator is often a point or a space. The problem with the point and the comma as either decimal mark or digit group separator is that, internationally, they have both often been used for both meanings, and their meaning is context-dependent (one must know which notational system is being used in order to interpret them). Therefore the space is recommended in the SI/ISO 31-0 standard,[10] and the International Bureau of Weights and Measures states that "for numbers with many digits the digits may be divided into groups of three by a thin space, in order to facilitate reading. Neither dots nor commas are inserted in the spaces between groups of three".[11] Other style-defining bodies are also moving toward this clearer notation. For example, the International Union of Pure and Applied Chemistry (IUPAC) suggest never using 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."[12] The American Medical Association, whose AMA Manual of Style is widely followed in health professions literature, also endorses a space for digit group separator.[9] (Specifically, a thin space is endorsed for typesetting; a regular word space is sufficient wherever typographical nicety is impractical.) The United Kingdom Metrication Board also proposed this system for Metrication in the United Kingdom and, while not universally adopted, it is the standard in the UK construction industry.
The International Bureau of Weights and Measures states that "when there are only four digits before or after the decimal marker, it is customary not to use a space to isolate a single digit".[11] Some manuals of style 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), whereas others use thousand separators, and others use both. For example, the Publication Manual of the American Psychological Association stipulates a thousands separator for "most figures of 1,000 or more" except for page numbers, binary digits, temperatures, etc.
There are always common-sense exceptions to digit grouping, such as postal codes, page numbers, and ID numbers of predefined nongrouped format, which style guides usually point out.
In binary (base 2), a full space can be used between groups of four digits.
Similarly, in hexadecimal (base 16), full spaces are usually used to group digits into twos.
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 mark and programs that have been carefully internationalised will follow this, but some programs ignore it and a few are even broken by it.
Countries where a dot is used to mark the radix point include:
Countries where a comma is used to mark the radix point include:
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 mark 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.[15][16][17]
The following examples show the decimal mark and the thousands separator; the lists are ordered chronologically, by when each country adopted the use:
| Hindi (Transliteration) | Value |
|---|---|
| एक (Ek) | 1 |
| दस (Das) | 10 |
| सौ (Sau) | 100 |
| सहस्त्र (Sahastr) / हजार (Hazaar) | 1,000 |
| लाख (Lakh) | 1,00,000 |
| करोड़ (Crore) | 1,00,00,000 |
| अरब (Arawb) | 1,00,00,00,000 |
| खरब (Kharawb) | 1,00,00,00,00,000 |
| नील (Neel) | 1,00,00,00,00,00,000 |
| पद्म (Padma) | 1,00,00,00,00,00,00,000 |
| शंख (Shankh) | 1,00,00,00,00,00,00,00,000 |
| महाशंख (Mahashankh) | 1,00,00,00,00,00,00,00,00,000 |
| Indian English | Value |
|---|---|
| One | 1 |
| Ten | 10 |
| Hundred | 100 |
| Thousand | 1,000 |
| Lakh | 1,00,000 |
| Crore | 1,00,00,000 |
| Thousand Crore | 1,000,00,00,000 |
| Lakh Crore | 1,00,000,00,00,000 |