Decimal separator

The decimal separator is a symbol used to indicate the separation between the integer part and the fractional part of a decimal number.

Point (.) Coma (,) Both, officially or commonly, or apostrophe (') Momayyez (High-Arab Commission) ()) No data

The International System of Units (SI) and the ISO 80000 standard currently admit two symbols: the comma and the period. Until 2003, the General Conference on Weights and Measures (CGPM) recommended the comma, but that year it decided to admit both signs, while remembering that there are other international standards that establish the comma as the only sign in all languages. For its part, the other standard on writing symbols, ISO 80000-1, from 2009, also admits both signs and cancels the previous recommendation of the comma of ISO 31-0. In any case, neither of these two signs is appropriate as a thousands separator: «numbers can be grouped three by three to facilitate reading; but neither commas nor periods should be used in the spaces between groups".

For their part, the Academies of Language recommend in the Spelling of the Spanish language: «In order to promote a process tending towards unification, the use of the point as a separator sign is recommended of decimals". However, they still consider the use of the comma valid, a sign that they recommended until 2010,^{[citation required]} as stated in the Pan-Hispanic Dictionary of Dudes from 2005 (in the article "Comma": "In numerical expressions written with figures, international regulations establish the use of the comma to separate the integer part from the decimal part").

History

The oldest known European text that uses the period as a decimal separator is the Compendium of the Abacus, published in 1492 by the Italian mathematician Francesco Pellos. Some historians refer to Bartholomew Pitiscus, a German mathematician, as the originator of the dotted decimal notation, but other historians allege that this was the medieval custom of adding punctuation marks to numbers in the middle of texts. In addition, Pitiscus used other decimal notation systems, so it is doubtful that the point was used expressly as a decimal separator, considering the other uses of the point throughout his work.

In 1579, the Frenchman François Viète (in his work Canon) introduced the use of a comma or a vertical bar as a decimal separator.

In 1582, the Belgian mathematician Simon Stevin (1548-1620) introduced a very unique notation. Where we would write 123.4567, he would write

123(0) 4(1) 5(2) 6(3) 7(4)

thus symbolizing 123 integer units, 4 first-order decimal units (tenths), 5 second-order decimal units (hundredths), 6 third-order decimal units (thousandths), 7 fourth-order decimal units (ten-thousandths).

Ten years later, the Swiss Jost Bürgi simplified the notation by removing the useless mention of the order of consecutive decimal fractions and putting the º sign above the units digit:

123♥ ♥ 45{displaystyle 12{breve {3}} 45,}

The same year, the Italian Magini replaced that little circle with a dot that he placed between the number of units and the number of tenths. This is how the notation that is still used today in Anglo-Saxon countries was born:

123.45{displaystyle 123.45,}

As for the decimal point, it was devised at the beginning of the XVII century by the Dutch mathematician and optician Wilbord Snellius (1580-1667), also known as Willebrord Snell and Willebrord Snel van Royen:

123,45{displaystyle 123{,}45,}

In 1617, the Scottish mathematician John Napier (in his Rhabdologia) used both the comma and the period, although in his all-important table of logarithms he used the decimal point in particular. For Florian Cajori, a mathematical historian, in his book A History of Mathematical Notations (1928), from this moment "mathematicians have been wavering in this matter ever since".

In the 18th century the use of the decimal point spread throughout continental Europe, while in the British Isles the decimal point became standard in usage, perhaps influenced by Napier's work. At the beginning of 1700, the mathematician Leibniz proposed the point as a multiplier, a proposal that was well received, since in Europe the comma was normally used as a decimal separator. On the other hand, in England the letter X continued to be used as a multiplier, which prevented this letter from being used, for example, in 3-dimensional XYZ calculations, as it confused mathematics students.

As early as 1771, the Encyclopedia Britannica recorded the use of the decimal point in its entry “Arithmetick”. To avoid their confusion of the dot as a multiplier and the dot as a decimal separator, they used the dot at the base (bottom) as a multiplier and the middle dot (·) to separate decimals.

In the United States, however, a nation newly independent from the British Empire in 1776 and sovereign in its decisions, they refused to use these different signs. It was not until the year 1900 that the American Committee of Mathematicians meeting in plenary session recognized the use of the letter X in mathematics and the need to use the middle dot (middle dot) as a multiplier and the low point as decimal separator, quite the reverse of British usage.

Current use

Use on computers

Unlike the staunch defense in 1991 of the presence of the letter Ñ on computer keyboards, the fight for the inclusion of the comma as a decimal separator in the number block is an issue that has not yet concluded.

For computers, decimals do not exist, only ones and zeros, so decimal numbers are an abstraction for humans and computers just represent them on screen or on paper as programmed. In modern operating systems, they have solved this with special characters called wildcards, thus depending on the regional configuration that the user chooses, the decimal separator will be represented by a point or a comma, as the case may be.

The drawback occurs in the so-called numeric block of the keyboard, which will always send the numeric code of the dot character to the respective computer. The solution implemented by the programmers of a popular operating system adds confusion to the European inhabitants, whose countries have several official languages. This solution is to interpret that exact key of the Number Block as the decimal separator implemented in the operating system, thus distorting what the user actually visualizes physically (a point) and that he has selected and pressed opportunely.

Computer Keyboard NEC PC-9801

A possible solution is to include the comma in the Numerical Block of the keyboards and to date the only ones that have presented a keyboard with such characteristics have been the Japanese in the NEC PC-9801 model, which even the company Microsoft recognizes it in its C language keyboard mapping.

Countries that use the decimal point

Among the countries that use the comma as a decimal separator are:

Countries that use the decimal point

Among the countries that use the point as a decimal separator are:

Hispanic-American usage

It is noteworthy that not all Latin American countries use the same convention regarding the decimal point or comma, and this is sometimes a reason for confusion and disagreement. However, the use of both is accepted by both the Royal Spanish Academy as by the International Office of Weights and Measures, responsible for the International System of Units (in its Resolution 10 of the 22nd General Conference on Weights and Measures of 2003).

Apostrophe

In countries like Spain it was customary to use the apostrophe or flown comma in a way that is homologous to the decimal comma in cases of handwriting, for example:

π π =3♫ ♫ 1416...{displaystyle pi =3^{prim}1416...}

Though this custom is no longer considered correct.

In machines and textbooks this custom is only followed occasionally, although it is rejected by the Language Academies and is not contemplated in international standards. Thus, in the Diccionario panhispánico de dudas of 2005 they establish, in the thematic article 'Comma': «The comma must be written in the lower part of the line, never in the upper part»:

π π =3,1416...{displaystyle pi =3{,}1416... !

Examples of use

The following examples are the decimal writing forms of the countries: