Numbers have functions that go beyond their application in arithmetic. They have other important roles as well.
Cardinal numbers
Cardinal numbers (Arabic numerals) are the ones usually learned early in foreign language, and they are the ones that are used in arithmetic expressions. Let’s look at their spelling.
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0 null
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10 zehn
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1 eins
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11 elf
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2 zwei
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12 zwölf
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3 drei
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13 dreizehn
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4 vier
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14 vierzehn
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5 fünf
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15 fünfzehn
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6 sechs
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16 sechzehn
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7 sieben
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17 siebzehn
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8 acht
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18 achtzehn
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9 neun
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19 neunzehn
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20 zwanzig
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30 dreißig
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21 einundzwanzig
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40 vierzig
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22 zweiundzwanzig
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50 fünfzig
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23 dreiundzwanzig
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60 sechzig
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24 vierundzwanzig
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70 siebzig
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25 fünfundzwanzig
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80 achtzig
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26 sechsundzwanzig
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90 neunzig
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27 siebenundzwanzig
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100 hundert
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28 achtundzwanzig
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1000 tausend
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29 neunundzwanzig
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1 000 000 eine Million
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From twenty through ninety, the second part of those numbers is added to the front of the number, as in the English nursery rhyme, “Four and twenty blackbirds baked in a pie . . .”
For numbers higher than a million, German differs from English. For example:
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1 000 000 000
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eine Milliarde
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one billion
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1 000 000 000 000
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eine Billion
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one trillion
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Also notice that thousands are separated in German by spaces, where in English they are separated by commas: for example, German 1 000 000 = English 1,000,000. However, decimals are separated by commas in German: for example, German 15,75 = English 15.75. It is said as fünfzehn Komma fünfundsiebzig. Finally, long numbers are rarely written out in words. If they are, they are written as one word: for example, 1055 = tausendfünfundfünfzig.
The four major arithmetic forms are addition (die Addition), division (das Teilen), multiplication (die Multiplikation), and subtraction (die Subtraktion). Also, equations are expressed in the following two ways:
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5 + 3 = ?
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Wie viel ist fünf plus drei? or Wie viel ist fünf und drei?
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5 + 3 = 8
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Fünf plus drei ist acht. or Fünf und drei ist acht.
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Division equations are expressed like this:
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12 ÷ 3 = ?
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Wie viel ist zwölf geteilt durch drei?
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12 ÷ 3 = 4
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Zwölf geteilt durch drei ist vier.
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Multiplication equations are expressed like this:
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10 x 3 = ?
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Wie viel ist zehn mal drei?
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10 x 3 = 30
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Zehn mal drei ist dreißig.
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Subtraction equations are expressed like this:
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22 – 11 = ?
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Wie viel ist zweiundzwanzig minus elf? or
Wie viel ist zweiundzwanzig weniger elf?
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22 – 11 = 11
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Zweiundzwanzig minus elf ist elf. Or
Zweiundzwanzig weniger elf ist elf.
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The currency of Germany as well as of most of Europe is der Euro (€). When stating the cost of something, the euros and cents are said separately and when written as numbers are separated by a comma.
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Es kostet 8,50 €. (acht Euro fünfzig Cent)
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It costs 8 euros 50 cents.
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22 – 11 = 11
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It costs 11 euros 25 cents.
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Ordinal numbers
When numbers become adjectives, they are called ordinal numbers. In English, the suffix -th is added to most numbers to make them ordinal numbers: for example, fifth, tenth, twentieth, and so on. German does something similar: it adds the suffix -te to numbers up to nineteen and the suffix -ste to numbers over nineteen. For example:
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zweite
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second
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fünfte
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fifth
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elfte
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eleventh
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neunzehnte
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nineteenth
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zwanzigste
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twentieth
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vierundzwanzigste
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twenty-fourth
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hundertste
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hundredth
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tausendste
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thousandth
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Three German ordinal numbers have an irregular formation. They are:
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erste
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first
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dritte
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third
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siebte
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seventh
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Since ordinal numbers are adjectives, they must conform to the gender, number, and case of the noun they modify. For example:
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der vierte Satz
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the fourth sentence
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von seiner ersten Klasse
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from his first class
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mit ihrem zweiten Mann
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with her second husband
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Let’s look at two examples in all the cases.
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nominative
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der zehnte Wagen the tenth car
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meine erste Freundin my first girlfriend
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accusative
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den zehnten Wagen
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meine erste Freundin
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dative
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dem zehnten Wagen
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meiner ersten Freundin
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genitive
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des zehnten Wagens
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meiner ersten Freundin
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In the same way as adjectives, ordinal numbers decline differently with der words and ein words.
For example:
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dieses zweite Gedicht
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this second poem
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sein zweites Gedicht
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his second poem
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Fractions
Fractions are formed quite simply by adding the suffix -el to the stem of the ordinal number. For example:
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ordinal number
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stem
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fraction
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dritte
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dritt-
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Drittel
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a third
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sechste
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sechst-
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Sechstel
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a sixth
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zehnte
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zehnt-
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Zehntel
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a tenth
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Notice that the words for the German fractions are capitalized. They have become neuter nouns. When fractions are used to express measurement, the measurement (meter, centimeter, liter, etc.) is written together with the fraction: ein Viertelmeter. When the two parts—the fraction and the measurement—can be written as two words, the fraction is no longer capitalized: ein viertel Meter (a quarter of a meter).
A few fractions have a special formation that is used throughout the German-speaking world. They are:
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½
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ein halb
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one-half
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1½
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anderthalb, eineinhalb
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one and a half
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2½
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zweieinhalb
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two and a half
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4½
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viereinhalb
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three and a half
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¾
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drei viertel
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three-fourths, three quarters
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You must distinguish between die Hälfte and halb, both of which mean half. The former is a noun and is not an arithmetic fraction. The latter is an adjective and can be declined like any other adjective. For example:
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Wir haben das Brot in zwei gleiche
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We divided the bread in two equal halves.
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Hälften geteilt.
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Ich werde nur ein halbes Brot kaufen.
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I’m going to buy only half a loaf of bread.
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Telling time
Cardinal and ordinal numbers are also used for telling time in German. Look at these commonly used expressions for telling time. Notice that German, like English, sometimes omits the element of time, because it is understood: for example, It’s ten minutes after three or It’s ten after three.
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1:00
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Es ist ein Uhr. (Es ist eins.)
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2:00
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Es ist zwei Uhr. (Es ist zwei.)
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3:05
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Es ist fünf Minuten nach drei. (Es ist fünf nach drei.)
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4:10
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Es ist zehn Minuten nach vier. (Es ist zehn nach vier.)
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5:15
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Es ist Viertel nach fünf.
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6:20
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Es ist zwanzig Minuten nach sechs. (Es ist zwanzig nach sechs.)
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7:25
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Es ist fünf vor halb acht.
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8:30
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Es ist halb neun.
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9:35
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Es ist fünf nach halb zehn
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10:40
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Es ist zwanzig vor elf.
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11:45
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Es ist Viertel vor zwölf.
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12:50
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Es ist zehn Minuten vor eins. (Es ist zehn vor eins.)
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1:55
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Es ist fünf Minuten vor zwei. (Es ist fünf vor zwei.)
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Germans do not use A.M. or P.M. to designate the hours before and after noon. Instead, the twentyfour- hour clock that is often used in the military replaces A.M. and P.M. For example:
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3:15 A.M.
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drei Uhr fünfzehn
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6:30 A.M.
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sechs Uhr dreißig
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2:11 P.M.
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vierzehn Uhr elf
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10:40 P.M.
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zweiundzwanzig Uhr vierzig
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12:00 A.M. (midnight)
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vierundzwanzig Uhr (Mitternacht)
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12:38 A.M.
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null Uhr achtunddreißig
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Time is usually expressed after the preposition um when telling at what time something occurs.
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Der Bus kommt um zehn Uhr zwanzig.
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The bus arrives at 10:20.
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Um wie viel Uhr steht ihr auf?
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What time do you get up?
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Days of the week
The seven days of the week in German are very similar to their English counterparts:
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Sonntag
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Sunday
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Montag
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Monday
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Dienstag
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Tuesday
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Mittwoch
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Wednesday
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Donnerstag
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Thursday
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Freitag
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Friday
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Samstag or Sonnabend
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Saturday
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When you say that something occurs on a particular day, use the preposition an in the dative case. The days of the week are masculine, so when the preposition an combines with dem, it forms the contraction am.
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Kommst du am Freitag an?
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Are you arriving on Friday?
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Nein, ich komme erst am Sonntag.
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No, I’m not arriving until Sunday.
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Months and Dates
The German months of the year are also very similar to English:
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Januar
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January
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Februar
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February
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März
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March
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April
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April
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Mai
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May
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Juni
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June
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Juli
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July
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August
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August
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September
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September
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Oktober
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October
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November
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November
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Dezember
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December
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The preposition in with the dative case is used to express in which month something occurs. The months are masculine. Remember that the contraction im stands for in dem.
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In welchem Monat bist du geboren?
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What month were you born in?
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Ich bin im Oktober geboren.
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I was born in October.
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All the months can appear in the same kind of prepositional phrase with im: im Januar, im März, im Juli, im August, and so forth.
When the days of the week or the months of the year are used with numbers to express dates, the ordinal numbers are used with the appropriate declension. Use the nominative case to tell the date of a day of the week. Because the word Tag is masculine, the ordinal number is also used with the masculine.
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Montag ist der achte Mai.
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Monday is the eighth of May.
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Ist Mittwoch der Zwanzigste?
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Is Wednesday the twentieth?
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Freitag war der Einunddreißigste.
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Friday was the thirty-first.
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The dative case after the preposition an is required when expressing on what date something
occurs. For example:
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Am ersten Juni kommt er nach Hause.
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He’s coming home on the first of June.
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Ihr Geburtstag ist am Achten.
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Her birthday is on the eighth.
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Der Film läuft erst am Siebzehnten.
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The movie starts running on the seventeenth.
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Ordinarily, Germans do not write out the dates as words.
The first of June is written as der 1. Juni and on the seventeenth is written as am 17.
Notice that a period follows the date and identifies it as an ordinal number.
The first of June is written as der 1. Juni and on the seventeenth is written as am 17.
Notice that a period follows the date and identifies it as an ordinal number.
When expressing years, use the phrase im Jahre before the year. However, it is also common to state a year by itself. For example:
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Sie ist im Jahre 1988 geboren
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She was born in 1988.
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or Sie ist 1988 geboren.
Der Krieg endete im Jahre 1991. The war ended in 1991.
or Der Krieg endete 1991.
The preposition in alone is not used with years. Use im Jahre or no preposition at all.
When a day, month, and year are combined as one phrase, they are expressed in this manner:
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Sie erklärten ihre Unabhängigkeit
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They declared their independence on the
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am 4. Juli 1776.
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Fourth of July, 1776.
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The date is said as am vierten Juli. The year is said as siebzehnhundertsechsundsiebzig.