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When do we have to capitalize numbers or fractions of a number or a quantity when writing them out like in

Sie hatten erst drei Viertel/drei viertel/Drei Viertel des Weges zurückgelegt.
Es ist jetzt viertel/Viertel vor zwölf/Zwölf Uhr.
Wir treffen uns um viertel/Viertel nach eins/Eins.

Which version is correct? What are the rules that help me to decide when to capitalize?

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up vote 2 down vote accepted

Correct versions are:

Sie hatten erst drei Viertel des Weges zurückgelegt.

Es ist jetzt Viertel vor zwölf Uhr.

Wir treffen uns um Viertel nach eins.

The rules applying here are:

  • Cardinal numbers are written in lower case by default; they are capitalized only if used as nouns, denoting a digit (Duden, Rule 78);

  • Ordinal numbers and fractions have to be capitalized if used as nouns (Duden, Rule 80).

So the rule of thumb may be: Cardinal numbers in lower case, fractionals capitalized. But beware of the exceptions (only two examples here, there are many more…):

Für den Teig benötigt man drei viertel Liter Milch... (or: drei Viertelliter)

Er setzt all sein Geld auf die Zwölf.

Canoo has a nice compliation of the rules about capitalisation of numbers with hyperlinks to the respective "official" rules.

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Since "Viertel" is a noun, it is capitalized if used as such, this means if you could add an article, it is capitalized.

Sie hatten erst drei Viertel des Weges zurückgelegt.

because you could write

Sie hatten erst die drei Viertel des Weges zurückgelegt.

In the sentence

Es ist jetzt Viertel vor zwölf.

you also could add an article:

Es ist jetzt ein Viertel vor zwölf.

But according to new German orthography, "viertel" is not capitalized if you cannot add an article:

Es ist jetzt viertel zwölf.

Look here.

In this sentence, "viertel" is used like a numeral.

Numerals, if used as such (and not f.ex. as a noun), are not capitalized (as in the sentences above).

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