Decimal separator

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

The use of a decimal separator developed from the use of place value systems that were introduced by the Sumerians in the 18th century BC. Were used. From the resulting possible fractions, the separation of the whole number part from the fractional part of a number developed. When using the decimal fraction notation, the denominator was omitted over time and the fractional part was separated from the integer by different notations.

In addition to the decimal separator, there is also the thousands separator , which improves the readability of large numbers by grouping the digits into groups of three.

development

In ancient Chinese mathematics (for example in Li Jan ') the fractional part was marked by subscripted numbers, for example for 123.45. ${\ displaystyle 123_ {45}}$

Around 1400, Jamjid Masʿud al-Kashi wrote the whole number part in black ink and the broken part in red ink. The first known source for the use of a decimal point is the 1492 Compendio del Abaco by Francesco Pellos , an Italian mathematician. So, based on the example, he simply writes 123.45.

Furthermore, different methods of representation are used for decimal numbers with fractions, for example François Viète used different notations in the Canon in 1579 , using the comma as a thousand separator:

${\ displaystyle 12 {,} 345 {,} {\ frac {678 {,} 901} {1 {,} 000 {,} 000}} \ quad 12 {,} 345 {,} {\ frac {678 {, } 901} {\,}} \ quad 12 {,} 345 {,} _ {678 {,} 901} \ quad 12 {,} 345 \ vert _ {678 {,} 901}}$ for 12,345,678,901 with a decimal point between 5 and 6

In 1593, Christophorus Clavius used the point as a decimal separator in sine tables and in 1595 Bartholomäus Pitiscus in his trigonometria . In 1617, John Napier first used the comma as a decimal separator in the Rhabdologia , then later the period, especially in his logarithmic tables , which were widely used. In the following period, the decimal point was predominantly used in textbooks and among experts, from Johannes Kepler to Henry Briggs , Adriaan Vlacq (1600–1667) and Jérôme Lalande (1805).

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

The decimal point can also be found in Joseph-Louis Lagrange (1808) and in the German translation of the Introductio in Analysin Infinitorum by Leonhard Euler , made by H. Maser in 1885. In Meyers Konversations-Lexikon (1888–1890, 4th edition) there is a notation with the comma as a thousand separator and as a decimal separator, the fractional part of the number is set smaller.

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

In countries where the decimal point is used, a space is often used as a grouping symbol. If the decimal point is used, the comma is often used as a thousand separator. In 1798, during the French Revolution, Auguste-Savinien Leblond recommended the semicolon (;) as a decimal separator so that the comma could be used as a thousand separator.

The current state of development has led to a standardization that is specified in the notation of numbers # decimal and thousand separators .

Point countries

• ﻿Point countries
• ﻿Comma countries
• ﻿Momayyez lands
• ﻿unknown
• Countries that use a period (.) As a decimal separator:

Comma countries

Countries that use a comma (,) as a decimal separator:

Others

Switzerland

In Switzerland, the use of a period or comma as a decimal separator is inconsistent; both are usually always read as a “comma”. A non-uniform practice is also followed in schools: the schools in the cantons of St. Gallen and Zurich teach the decimal point, for example. It happens that in the lower level / primary school the comma (as it is spoken) is taught, but from the intermediate level on the point is taught.

In accordance with the instructions of the Federal Chancellery , the comma is generally used in official federal documents , but a point is placed between the currency unit and the sub-unit for amounts of money. The same is true in other countries, so many systems allow the definition of a special monetary decimal separator, independent of the numeric decimal separator . The Federal Office for Topography also uses the point for the Swiss national coordinates .

In the IT sector, in today's operating systems (Windows, macOS, Linux, etc.), the point is defined as a decimal separator in the Swiss-specific language setting; the point is also used on the numeric keypad of Swiss keyboards.

Neither point nor comma are used as a thousand separator. Unless a protected space is used as the thousands separator, the (even) apostrophe (') is used.

Arabian Peninsula and Iran

٫
Momayyez

In the Arabian Peninsula and Iran , the momayyez (٫) is used as a decimal separator.

International standards

According to international standards ( International System of Units (SI), which follows the General Conference on Weights and Measures ; ISO 80000-1 of the International Organization for Standardization (ISO) , which also follows the General Conference on Weights and Measures), the decimal separator is either the comma or the Point - whereby this statement in EN ISO 80000-1 is provided with the comment: "In accordance with the ISO / IEC directives ... the decimal point in international standards is a comma on the line". In addition, according to EN ISO 80000-1, the point as a multiplication symbol and the decimal point should not be used together.

In the International Spelling Table , the decimal separator is always specified with the keyword decimal .

Omission of the zero in front of the decimal point

Tantalum electrolytic capacitor with a capacity of 1.0  µF

In the English-speaking world, with an absolute value of a number <1, ​​the zero in front of the decimal separator is occasionally left out. B. writes ".35" instead of "0.35". According to the international rule for this case “there must be a zero in front of the decimal point.” The omission of the zero in front of the decimal separator is also possible and common when programming and entering data on computers and pocket calculators . For reasons of space, the values ​​on small electronic components are also often given without a preceding zero.

A special feature here is often that the decimal point is replaced by the SI prefix symbol of the value unit. This makes it easier to read the value while eliminating the risk of missing the decimal point due to the tiny font and often poor printing. The value of the capacitance on the tantalum electrolytic capacitor in SMD design in the adjacent picture reads “1µ0” with the meaning 1.0  µF .

Individual evidence

1. The South African measurement system and its origin ( Memento from March 17, 2013 in the Internet Archive ) (English; PDF , ≈ 56  kB ) - formerly on EE Publishers , on German the South African measurement system and its origin , published in April / May 2011, last saved in the Internet Archive on March 17, 2013.
2. 6.5 Groups of numbers - European Publications Office , on Interinstitutional Rules for Publications , last change on May 24, 2011; see also (English) 6.5. Punctuation in figures , last change on April 22, 2015.
3. Mathematics syllabus ( memento of the original from September 24, 2015 in the Internet Archive ) Info: The archive link has been inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. (PDF; ≈ 257 kB) - on schule.sg.ch , edition 2008, accessed on February 28, 2016.
4. writing instructions ; 514: Decimal comma and decimal point ( memento of the original from January 22, 2017 in the Internet Archive ) Info: The  archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. - Editor: Federal Chancellery , 2nd updated edition 2013, p. 80, last change on August 24, 2015.
5. New coordinates for Switzerland - The frame of reference LV95 ( Memento of November 4, 2011 in the Internet Archive ) (PDF, ≈ 3.4  MB ) - 1st edition at the Swiss Federal Office for Topography , published in November 2006, last saved in the Internet Archive on November 4, 2011.
6. E.g. for Apple keyboards see Identifying the local keyboard on support.apple.com
7. International Bureau of Weights and Measures (ed.): Le Système international d'unités . 8th edition. 2006, 5.3.4: Écriture des nombres et séparateur décimal, p. 44 (French, bipm.org [PDF; accessed January 24, 2009]).
8. Résolution 10 de la 22 e réunion de la CGPM (2003). International Bureau of Weights and Measures , accessed November 29, 2008 (French).
9. a b EN ISO 80000-1: 2013, sizes and units - Part 1: General , chap. 7.3
10. In the "National Foreword" of DIN EN ISO 80000-1 it says: "In German-speaking countries, the comma is the decimal point".
11. Appendix 14 ( Memento of July 6, 2011 in the Internet Archive ) of the Implementing Regulations for the Radio Service