Decimal mark

The decimal point ( for example, the decimal or the decimal point ) is in the decimal system, a character indicating the boundary between the integer part and the fractional part of a number.

The use of a decimal evolved from the use of value systems that have been used by the Sumerians in the 18th century BC. From the consequent possible breakage notation, the separation of the integer part from the fractional part of a number developed. When using the Dezimalbruchschreibweise the denominator of the fractional part was omitted and the time are separated by different spellings from the integer.

In addition to the decimal point, there are also the thousands separator ( in Germany not umbrechendes " nonbreaking space " ), the readability of large numbers improved by the digits are grouped in threes.

Development

In the ancient Chinese mathematics (for example, Li Jan ' ), the broken part was characterized by lower set numbers, so for example for 123.35.

By 1400 Jamshid Mas ʿ ud al - Kashi wrote the integer part with black ink, the broken part with red ink. The first known source for the use of a decimal point is then in 1492 the font Compendio del Abaco by Francesco Pellos, an Italian mathematician. So he writes, based on the example, just 123.35.

Furthermore, different modes of representation for decimal numbers are used to break, such as used in Canon 1579 François Viète different notations, which he used as the thousand separator comma:

Christopher Clavius ​​in 1593 using sine tables and Bartholomew 1595 Pitiscus in his Trigonometria the point as a decimal separator. John Napier put 1617 in the Rhabdologia as decimal only the comma, then later to the point, especially in his logarithm tables, which spread widely. In the following period, the decimal point was in the textbooks and among professionals mainly used by Johannes Kepler, Henry Briggs, Adriaan Vlacq (1600-1667) and Jérôme Lalande (1805 ).

In the 18th century came in continental Europe in everyday use and teaching, however, increasingly the decimal point on, Friedrich L. Bauer suggested here French influence. It found its way mainly in popular science books ( examples are: Abraham Gotthelf Kästner 1758, Joseph Spengler 1779, Christian Ludwig Ideler 1831, Martin Ohm 1829).

Even when Joseph -Louis Lagrange (1808 ) and in the German translation of the Introductio in Analysin Infinitorum by Leonhard Euler, which was carried out by H. Maser 1885, we find the decimal point. In Meyers Lexicon (1888-1890, 4th edition ), there is a notation with the comma as the thousands separator and the decimal point, the fractional number portion is set smaller.

In the English -speaking world, the point remains the predominant decimal point. The word decimal point (decimal point) is mentioned in the 1771 Encyclopædia Britannica chapter Arithmetick.

In the countries where the decimal point is used, it is often taken as a grouping character a space. If the decimal point is used, the comma is used as the thousands separator. 1798, during the French Revolution, recommended Auguste- Savinien Leblond the semicolon as the decimal separator, so that the comma could be used as a thousands separator.

Point countries

• Point countries
• Comma - countries
• Momayyez countries
• Unknown

Countries that use a point as decimal separator:

• Australia, Botswana, China, Costa Rica, Dominican Republic, El Salvador, Guatemala, Honduras, Hong Kong, India, Ireland, Israel, Japan, Korea ( North and South), Malaysia, Malta, Mexico, Namibia, Nicaragua, Nigeria, New Zealand, Pakistan, Panama, Philippines, Singapore, Taiwan, Thailand, United Kingdom, United States

• Regional: Canada ( English-speaking )

Comma - countries

Countries that use a comma as decimal separator:

• Albania, Andorra, Argentina, Belgium, Bolivia, Brazil, Bulgaria, Chile, Denmark, Germany, Ecuador, Estonia, Faroe Islands, Finland, France, Georgia, Greece, Greenland, Indonesia, Iceland, Italy, Colombia, Kosovo, Croatia, Cuba, Latvia, Lithuania, Luxembourg, Macedonia, Moldova, Netherlands, Norway, Austria, Paraguay, Peru, Poland, Portugal, Romania, Russia, Sweden, Serbia, Zimbabwe, Slovakia, Slovenia, Spain, South Africa, Turkey, Ukraine, Hungary, Uruguay, Venezuela, Belarus

• Regional: Canada ( French-speaking )

• Official Journal of the European Union (otherwise also the point can be used in English, Irish and Maltese texts)

Others

Switzerland

In Switzerland, the use of dot or comma as the decimal separator is uneven; both are usually always read as " comma". Even in schools a non- uniform practice is followed: The schools of the Canton of St. Gallen as well as the Canton of Zurich teach, for example, the decimal point. It happens that in the lower school / primary school, the comma ( as it is spoken ), is taught from the intermediate point.

In official documents of the Federation, the comma is used in accordance with the instructions of the Federal Chancellery in principle, but a point is monetary thresholds set between the monetary unit and subunit. The point also used the Swiss Federal Office of Topography for the Swiss coordinates.

Many word processing programs in Switzerland specific language setting of the point is defined as the decimal separator, the point is on the numeric keypad Swiss keyboards also used.

But when thousands separator neither point nor commas are used. Insofar as the thousands separator is not a space is set for this comes the (straight) apostrophe used.

Arabian Peninsula and Iran

On the Arabian peninsula and Iran, the so-called Momayyez (. ) Is used as the decimal separator.

International standards

According to international standards ( International System of Units (SI ), which follows the General Conference of Weights and Measures; ISO 31-0 of the International Organization for Standardization ( ISO), which is also the General Conference on Weights and Measures follows ) is the decimal either the comma or point. In addition, according to ISO 31-0, the point to be the mark and the decimal point can not be used together.

Omission of the zero before the decimal point

In the English -speaking world, the zero is omitted occasionally before the decimal point, so that a notation like .35 occurs on continental Europe, this is not common, and it is 0.35 or even 0.0 written, which developed the jocular no time.

Software versions

In the name of software versions, the notation is used with point (eg Windows 5.1) in German. However, this is not a decimal point, but an outline, as the example Linux 2.6.39.4 shows. It may be that the number of groups have different meanings. In the example Linux, the second group of numbers increased in versions with new features. In bugfix releases, so new Linux versions, the only fix errors but increases the third set of numbers. The costs arising from increasing numbers here may also be greater than 9.