A Half, Half A And Half An

All of these expressions are completely acceptable.

• Could I have half a pound of butter? / Could I have a half pound of butter?
• I waited for half an hour.
• The dog eats a half pound of hamburger every day. / The dog eats half a pound of ….

Note the expression ‘a half bottle’. This is used to refer to a half-sized bottle of wine or spirits.

Avoid expressions like a half a and a half an.

• He had half an orange. / He had a half orange. (BUT NOT He had a half an orange.)

You can learn more about half here.