Learn German: Die Flasche enthält einen halben Liter.

In German, halb acts as a regular adjective. It must follow the article and take standard adjective endings. So instead of "half a litre", German literally says "a half litre".

Why does halb take the -en ending here?

The phrase einen halben Liter is the direct object of the verb enthalten (to contain), which puts it in the accusative case. Since Liter is a masculine noun in the accusative case, the adjective following the indefinite article einen must take the -en ending.

If we wanted to say "half a litre of water", how would we add "water" to this sentence?

You would simply add Wasser to the end: Die Flasche enthält einen halben Liter Wasser. When specifying a material after a measurement, German typically uses a partitive apposition. This means the material directly follows the quantity without any translation for "of" and takes no special case ending.

Could we use the partitive genitive here and say einen halben Liter des Wassers?

You would only use the genitive here if you were referring to a specific, previously defined amount of water (meaning "half a litre of THE water"). For general, unspecified materials like "water" in general, you must drop the article and use the partitive apposition directly: Wasser.