The expressions a half, half a and half an are all completely acceptable.
- Could I have half a pound of oranges? / Could I have a half pound of oranges?
- Joe has half an apple. / Joe has a half apple.
However, expressions like ‘a half a’ and ‘a half an’ are completely unacceptable.
Don’t say or write:
- I have a half an orange.
Note that the expression one and a half is plural.
- I waited for one and a half hours. (NOT I waited for one and a half hour.)
Or you can say: I waited for an hour and a half.