# Spelling of numbers

The spelling of numbers or the structure of numbers describes how numbers are notated in the decimal system . For example, it regulates which characters are used as decimal separators, i.e. to separate the integer from the fractional part, and how sequences of several digits are grouped , for example with a thousand separator .

## Decimal and thousand separators

### Germany and Austria

#### Decimal separator

In Germany, the DIN standards DIN 1333 (numerical data), DIN 5008 and now the international EN ISO 80000–1 deal with the spelling of numbers. In Austria, the regulation of the spelling of numbers in the Austrian dictionary (ÖWB) and in ÖNORM  A 1080 (guidelines for text design) and also in EN ISO 80000−1.

The comma (,) is used as the decimal separator .

#### Thousands separator

To make it easier to read numbers with many digits, they “may” be divided into groups of three. If such a subdivision is used from the position of the decimal separator to the left, “can” (DIN 1333) or “should” (DIN 5008) or “must” (EN ISO 80000) are used to group spaces . For numbers with decimal places (broken part), this also applies to the right of the decimal separator. DIN 1333 expressly does not provide for the use of the point (.) To separate thousands ; EN ISO 80000 excludes any character except the small space as a separator. The Duden adopts the spelling of numbers from the DIN standards, i.e. also specifies the space to separate thousands. There must be no line break within a number. In Austria, according to the above guidelines, the space is also used as a thousand separator.

Exceptions to the classification rules are for both Germany and Austria:

• special numbers such as years and postcodes
• Bank codes , IBAN , telephone numbers , ISBN and others for which special classification rules exist
• Ordinals that are used as a measure, e.g. B. EN ISO 80000-1
• Amounts of money; see below
Examples of notation
• Comma as decimal separator:
• 0.5
• 9,765 m
• € 12.45
• Four-digit numbers are often not yet treated as numbers with many digits and then remain unorganized (except in Austria or except in tables with higher numbers):
• 4321 or 4 321
• 7,654,321,123,456
• 126,512 inhabitants, but only 6,630 children (but Austria: 6,630 children)
• Diameter of the earth at the equator: 12,756.2 km

For compatibility reasons , a normal non-breaking space is often used instead of the narrow space .

In the case of monetary amounts, both spaces and periods with the fixed width of a digit can be used as a thousand separator; The currency symbol is to be placed after the number in the running text (Austria: in front of the number):

• 7654 321.12 € (Austria: € 7,654 321.12 ) or
• € 7,654,321.12

According to DIN 5008, for security reasons, amounts of money should be structured with a point, in the running text with a variable width.

### Switzerland and Liechtenstein

The use of a point or comma as a decimal separator, as well as the thousands separator, is not regulated uniformly in Switzerland and Liechtenstein .

#### Decimal separator

In accordance with the instructions of the Swiss 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 monetary amounts.

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 from the middle level onwards as the point. In schools, the comma is used in handwriting.

In many operating systems, 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. For example, values ​​with a decimal point are displayed in Excel tables. The Federal Office for Topography also uses the point for the Swiss national coordinates .

Colloquially, a comma is usually used : the box weighs three point six kilos . When it comes to accuracy, e.g. B. when dictating for the purpose of entering into a computer, is represented as follows: three decimal point six .

#### Thousands separator

In official publications of the Swiss Federal Chancellery, the fixed spacing (protected space) is used to break down longer sequences of digits into blocks of three. Furthermore, numbers (except in the case of tabular representation) should only be subdivided from five digits.

Especially outside of professional typography, the straight apostrophe '(Unicode `U+0027`) is often used - always handwritten ; this also corresponds to the Windows and Mac standard settings. The typographic apostrophe '( `U+2019`) is rarely used as a thousand separator.

#### Examples

description Swiss Federal Chancellery Canton St. Gallen curriculum
or IT area
12 0.5 0.5
length 9.76 m 9.76 m
Amount of money, fraction CHF 10.2 million CHF 10.2 million
Amount of money, written out Fr. 7 654 321.10 CHF 7,654,321.10
Diameter of the earth at the equator 12,756.2 km 12,756.2 km

### International standards

#### ISO

The International Organization for Standardization (ISO) defines the spelling of numbers in the ISO 80000 series of standards (sizes and units) . According to this standard, numbers can be divided into groups of three for better readability, both to the left and to the right of the decimal separator. This thousand separator should be a thin space , never a comma, period or any other character.

ISO 80000-1 provides a comma or a point on the line as a decimal separator , whereby this statement in DIN EN ISO 80000-1 is provided with the comment: “In practice, the choice between these alternatives depends on the usual usage in the respective language from. ”Furthermore, the national foreword of DIN EN ISO 80000-1 says:“ In German-speaking countries, the comma is the decimal point ”.

For the creation of standards, the ISO, in accordance with ISO / IEC Directives , stipulates the comma as a decimal separator for all language versions.

#### CGPM

In 1948, the 9th  General Conference on Weights and Measures ( Conférence Générale des Poids et Mesures , CGPM) decided in resolution 7 that numbers could be divided into groups of three digits each to make reading easier; under no circumstances are the groups separated by periods or commas.

Regarding the decimal separator, this resolution says: In numerical values, the comma (French custom) or the point (British custom) are only used to separate the integer part from the decimal part of the numerical value. At the 22nd CGPM, this recommendation was confirmed and specified to the effect that the point should be set at line height. It also states that some international (standardization) organizations recommend the comma as the sole decimal point in all languages; in this respect, preference is given to the comma.

## Unit of measurement

If the number is followed by a unit symbol (cm, km, ° C) or if there is a currency symbol (€, \$, ¥, £ etc.) in front of / behind a number , this symbol is separated by a protected space or a protected narrow space in the computer set to connect.

The unit symbols ° ( angular degrees ), ′ ( angular minutes ) and ″ ( arc seconds , inches ) are excluded from this rule , in which no space is inserted between the number and the unit symbol.

## Rounded numbers

Often, for example in measurement technology , numbers and measured values can only be specified up to a certain error limit or measurement uncertainty . That is why a point must be specified for the communication of calculation and measurement results in science and technology, at which it must be rounded off in order not to pretend greater accuracy than what is actually available.

Laying down the rounding position whose value is W to determine which is an indication, such as 1 (one), 0.1 (tenth), 0.01 (hundredth), etc. The control at a known error limit or uncertainty u is

u / 30 < Wu / 3

Example: u = 0.6; u / 30 = 0.02 < Wu / 3 = 0.2; W = 0.1; so the rounding place is the tenth place.

12.345 ± 0.6 becomes 12.3 ± 0.6

According to DIN 1333, the comma must not be further to the right than immediately to the right of the rounding point, so that digits to be omitted by rounding are not replaced by zeros (or other digits). If necessary, the decimal point must be shifted to the left and corrected at the same time by multiplying it by a power of ten; see examples under Measured Value and Significant Places . Significant digits are understood to mean all digits of a number from the first non-zero digit from the front to the rounding point.

In line with the rounded result, u is rounded up to a significant digit (the one furthest to the left) if there is one of the digits 3 to 9, otherwise to two digits; see examples under error limit .

## Notation for uncertainty

A notation like 12.3 ± 0.6 is common, but it can be mathematically misinterpreted as if it only means the values ​​11.7 and 12.9. However, it is used here to indicate a range that includes all values ​​from 11.7 to 12.9.

For the specification of the uncertainty, it is recommended to add the standard uncertainty to the result in brackets with values ​​like the lowest-value digits of the result, ie “12.3 (6)” for “12.3 with a standard uncertainty of 0.6”.

Another example based on the  value of the inverse fine structure constant 1 / α recommended according to CODATA 2018 shows the notation of the value including its standard uncertainty:

1 / α = 137.035 999 084 (21).

This form of expression is synonymous with

1 / α = 137.035 999 084 with u 1 / α = 0.000 000 021.

## Spelling out number names in running text

A previously established letterpress rule was to write out the numbers zero to twelve and their list form (first, second, third ...) in the running text generally not in numerical form, but with their numerical names . The Duden calls this rule outdated today, but it is often still followed (you can sometimes find different spellings in articles written by different editors in the same newspaper). Smaller numbers are also occasionally written in digits, for example for special emphasis and especially in technical and scientific texts. On the other hand, it is particularly easy to write larger numbers that can be reproduced with words. This is especially true for round numbers like twenty, one hundred, three thousand. Basically, numbers of the same type are written in the same way. In the sentence “There are 12 boys and 13 girls in class 5c”, both numbers can be written out, but the mixed form “twelve boys and 13 girls” is considered incorrect. The Duden recommends only spelling out numbers with one and two syllables (“She has fifteen [or: 15] cats”). If two numbers follow one another, write at least one of the two for better readability: “twenty eleven year old girls”, “twenty eleven year old girls”, “20 eleven year old girls”, but not “twenty eleven year old girls”. Numbers are usually spelled out at the beginning of a sentence.

In equations, the numerals (number word) form a separate part of speech , which in principle is written in lower case in the sentence . This is how you write: "Two plus three is (not: are ) five" or: "Here is the number seven". An exception is the substantive use of numbers by placing an article in front, such as in: "die five" or: "a zero" or: "a one" - here one capitalizes.

## Big numbers in word form

Where large numbers are exceptionally expressed in word form with their number names, the following rules apply:

Numbers up to 999 999 are written as one word. Example: 312 723 = three hundred and twelve thousand seven hundred and twenty three.

The powers of a thousand from the million (million, billion, trillion, trillion, etc.) are nouns and are written in correspondingly large numbers in word form as a single, capitalized word.

Example: 1 234 678 901 = one billion two hundred thirty-four million six hundred seventy-eight thousand nine hundred one

## Number-word combinations

Section 42 of the official spelling (2006) reads: "If combinations of digits and suffixes form the front part of a composition, a hyphen is placed after the suffix". For the naming of decades, however, z. B. the spelling "50s" is expressly permitted. "50s", "50s", "1950s" or "1950s" are equivalent as long as there is no risk of confusion with regard to the century. Alternatively, the decade can also be written out in full: "1950s".

## Handwritten spelling of numbers

As with handwriting, the handwritten spelling of numbers can often tell you the country of origin of the writer. In the English-speaking countries, the handwritten one only consists of a vertical line, and in the case of the seven, the middle crossbar is omitted - although there are individual exceptions. In the Scandinavian countries, the one is also written without a stroke; but at the seven the middle bar occurs.

Depending on the formative learning, different shapes of the individual digits occur.

• 1: The short coat above can be straight or curved downwards. The number below is rarely given a serif .
• 2: The curve above can lead straight or curved tangentially to the lower left, or to the center of the circumscribing rectangle. The straight or wavy horizontal line below can connect directly or via a loop with a loop angle of up to 270 °.
• 3: The upper belly can also be replaced as a horizontal line at the top and the following slash from top right to left to the middle of the height. The upper and lower abdomen can be connected by an approximately 270 ° loop.
• 4: The triangle can be open at the top to the fork, the left prong ends at an angle or straight, the right prong can be shorter or completely absent. The overhang to the right of the horizontal line halfway up is rather small and can be missing, the horizontal line can be curved in cursive script.
• 5: The lower left end of the line of the (lower) abdomen can taper off slightly upwards or downwards.
• 6: The free ending line above can be curved or straight and slightly different in the general direction.
• 7: The top or middle line can be curved instead of straight. The middle one can also be missing; in addition, the top line at the left end can have a small, serif-like spread.
• 8: Line of eight with a cross halfway up or two circles that are tangent. In cursive script, the upper circle can end in a loop at the top right.
• 9: Analog "6". Furthermore, the smear can also start with a small reverse loop on the right or even tangentially on the left of the circle.
• 0: Clearly oval or rather small and circular. For clear differentiation from the letter "O" with a slash struck through to the bottom left, for example in alphanumeric serial numbers. Just like the 8, in cursive fonts the zero at the top right can end in a loop.

“Half height” actually means a little higher, so that the lower “half” of top-bottom (almost) symmetrical digits is about 10% larger than the top, which indicates a stable stack like a small building block on a larger building block. However, the upper triangle of the "4" often measures more than half the height of the digits.

For some digits, the sequence and direction of the lines are varied. In the case of the digits with an infinite, closed line - 0 and 8 - the position (with "8" possibly: the positions) where the pen is attached can vary without it having to be visible on the completed number. The same applies to the direction of rotation of the lines.

## literature

• For more information, see the following articles in the Lexikon der Deutschen Sprachlehre: Upper and lower case (p. 67 ff.); Cardinal number, base number (p. 75); Numerale, number word (p. 108); Part of speech (p. 138 f.) As well as numbers and digits (p. 140)
• W. Ludewig, G. Wahrig, P. Kürten: Lexicon of German language teaching. In: Gerhard Wahrig : German Dictionary. Newly published by Renate Wahrig-Burfeind. 6th revised edition. Bertelsmann-Lexikon-Verlag, Gütersloh 1997, ISBN 3-577-10677-8 , pp. 37-144 (first edition: ibid. 1966).

## Individual evidence

1. a b DIN 5008: 2011-04 , writing and design rules for word processing
2. DIN EN ISO 80000-1: 2013-08, sizes and units - Part 1: General (ISO 80000-1: 2009 + Cor 1: 2011); German version EN ISO 80000-1: 2013 .
3. a b c Swiss Federal Chancellery (Ed.): Writing instructions . 2nd Edition. 2015, 5.1.3: Decimal, fraction and ordinal numbers, p. 80 ( [1] [accessed May 16, 2018]).
4. Mathematics syllabus ( memento of the original from March 23, 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. (PDF file; 252 kB) from schule.sg.ch , accessed on September 27, 2013
5. E.g. for Apple keyboards see Identifying the local keyboard on support.apple.com
6. Federal Office of Topography swisstopo (ed.): New coordinates for Switzerland - The frame of reference LV95 . 1st edition. 2006, p. 8–11 ( cadastre.ch ( memento of November 4, 2011 in the Internet Archive ) [PDF; accessed on October 27, 2010]). New coordinates for Switzerland - The LV95 frame of reference ( Memento of the original from November 4, 2011 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice.
7. ISO / IEC Directives Part 2, Section 6.6.8.1. Retrieved January 25, 2016.
8. ^ Resolution 7 of the 9th CGPM (1948) ( online , accessed June 30, 2019).
9. ^ Resolution 10 of the 22nd CGPM (2003) ( online , accessed June 30, 2019).
10. Guide to the Expression of Uncertainty in Measurement (GUM)
11. CODATA Recommended Values. National Institute of Standards and Technology, accessed July 30, 2019 . Value for inverse fine structure constant.
12. Writing numbers. In: Duden Newsletter. June 1, 2007, accessed April 29, 2012 .
13. German spelling - rules and dictionary. According to the recommendations of the German Spelling Council . Revised version of the official regulations 2004. Munich / Mannheim 2006, p. 46 ( Rechtsschreibrat.ids-mannheim.de [PDF] At the Institute for the German Language).