In English and in German there are cardinal numbers, used for counting, calculating and staring years and age. Ordinal numbers are used to order or rank things, giving the date as well as floors of buildings. 

1. Cardinal Numbers 

Below are the cardinal numbers in German. Keep in mind that in English we can say “a dog” (ein Hund), and “one dog” (ein Hund), using either the indefinite article “a/an”, or the cardinal number “one”. In German, the indefinite article “ein/eine/ein” and the cardinal number used when referring to one of something are the same. However, we need to pay attention to the gender and case of the noun. 

Example:
Das ist ein Hund. This is a / one dog.
Das ist eine Katze. This is a / one cat. 
(Note: You cannot say: “Das ist eins Hund/ eins Katze”)

Note: The teens could be translated to “threeten”, “fourten”, etc. 

Note: The literal translation of these numbers would be “one and twenty”, “two and thirty”, “three and forty”, etc. 

2. Ordinal Numbers

Ordinal numbers normally add ‘-te’ to the end of the spelling of the cardinal numbers less than 20, with a few exceptions. Ordinal numbers greater than 19 add ‘-ste’ to the end. Ordinals can precede nouns, which is why the definite articles are often used in combination with ordinal numbers.

Example:
Er hat die erste Prüfung bestanden. He has passed the first exam. 

When referring to dates, we add “am” (an dem), when referring to centuries or locations we add “im” (in dem). 

Example:
Halloween ist am einunddreissigsten Oktober. Halloween is on the 31st of October. 
Wir leben im einundzwanzigsten Jahrhundert. We live in the 21st century. 

Note: The ending “-te” or “-ste” doesn’t change, regardless of the gender of the noun, but we still need to use the correct article. For dates, we usually use “der”. 

Example:
Das ist der erste Geburtstag meiner Tocher. This is the first birthday of my daughter. 
Das ist das erste Auto. This is the first car. 
Heute ist der dreiundzwanzigste Oktober. Today is the 23rd of October.