Decimal mark#Digit grouping

Digit grouping refers to the grouping of digits in long numbers. In most modern languages ​​larger numbers in a place value system to the base are spoken thousand. There facilitate thousands separator the reading of large numbers, with the help of the digits of a number are starting grouped at the lowest point in groups of three.

  • 2.1 On the problem of point and comma for thousands and decimal
  • 2.2 On the problems in typography and computer set
  • 2.3 Representation in the programming

Methods of digit grouping

With the thousands separator

Widely used, the grouping of digits in a place value system of number representation in blocks of three, in the decimal ie in powers of thousands ( thousands separation).

In addition to the digits to the left of the decimal separator can also use the digits to the right of the decimal point, so the decimal places are grouped.

  • Example: 123 456 789.123 456 789

The breakdown of numbers in groups of digits for readability. It also simplifies the Germans and, for example, English speaking, since even here numbers are divided into groups of three: one hundred and twenty million, four hundred fifty-six thousand, seven hundred eighty-nine for the number 123 456 789

The division into three groups also facilitates working with the intentions of units, so the prefixes micro, milli, kilo, mega, etc. Each triple represents a number here one intent: 123 456 789 watt 123,456 789 megawatts or 123 456.789 kilowatts. The conversion to the technical notation is easy: 10 000 m = 10 km = p5031010 × 103 m.

Exceptions to the classification in groups of three for example, form postal codes or numbers which are subject to their own rules for structuring.

Relevant German standards DIN 1333, DIN 5008, ISO 31 international and his successor ISO 80,000. ÖNORM A 1080 For Austria, and the Austrian dictionary applies.

Digit grouping in numerical mathematics

Notwithstanding the thousands of blocks to group long sequence of digits in five blocks.

In addition to numbers with no decimal - aborting (eg, irrational numbers ) you are such as in astronomy the long strings of numbers for the orbital elements or ephemeris ( VSOP, ELP, JPL ) to.

Other number systems

In the Chinese number system as well as in East Asian cultures that have taken over this, is ten thousand (Chinese万/万, wan Pinyin ) is the largest elementary number word and basic number for specifying larger numbers. Large numbers are therefore read in blocks of 4 digits. A division into three blocks helps in such languages ​​in no way read. This has the consequence that for Mehrsprachler simultaneous compiling large numbers is not easy, for example, between Chinese and English.

In the Indian number system, it is common to first group the three lowest points and then at two points each, and giving numbers independent elementary name. So the spelling 10'00'000 and the term is used about 10 lakh for a million.

Character for the digit grouping

Were as grouping character, and are used in different countries and languages ​​different characters:

  • Narrow space ()
  • Space ()
  • Dot (.)
  • Comma (,)
  • Single quotation mark (')
  • Apostrophe (')

On the problem of point and comma for thousands and decimal

According to German and international standards, the narrow space to be used as a thousands separator (eg 123456789 ). In addition to the standard conformity, the space has the advantage that it can not be confused with the decimal point in international communication. However, the disadvantages are a subjectively worse readability and especially the unwieldy because (protected ) narrow spaces - for example, on keyboards with German key assignment - not by a single (combined) keystroke can be entered.

Traditionally, the dot as thousands separator and the comma as the decimal separator was used in Germany, Austria and France. This is also the default setting for the German spelling in various programs, such as LibreOffice or Microsoft Office. In contrast, the two characters are used the other way around as in England:

  • Germany, Austria, France: 123456789.123
  • England, USA: 123,456,789.123

A number such as 12.345 therefore can not be correctly interpreted without further notice. For this reason, standards see the use of a space as the thousands separator before (DIN 1333, DIN 5008 and ISO 31 ). It is recommended a narrow space if this is technically available.

Sometimes (for example in Switzerland), the digits are separated from each other with an apostrophe to eliminate the aforementioned problems with comma and period equal to:

  • Example: .123 or 123'456'789 123'456'789, 123

Here the point or the comma has a unique meaning.

On the problems in typography and computer set

For the digit grouping is used typographic white space that should be narrower than the normal word spacing. Often it is 1/6 em (quad ) is recommended. An exact standardization is missing.

For a presentation in the computer record ( Webtypographie ) a nonbreaking space is necessary to prevent a line break within the numeric column. Alternatively umbrechender Space are protected before the break by assigning a nowrap attribute. The excessive width of the standard space character can by scaling, or a manual letter spacing, thus blocking the number, be corrected, or by replacement with various smaller spaces - but lacking throughout the widespread implementation in pleadings or programs.

In TeX and LaTeX are large (5/18 em ) and small gap (3/18 em ) in the form a \ b or a \, b are available.

Representation in the programming

The problem is to group digits in programming languages. In a few languages ​​( for example, in Perl, Ruby and Verilog ), it is possible to group numbers when required using the underscore character ( _), in most other programming languages ​​is a correspondence not to be found.

Myriad Thin space Full stop
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