I agree with doninbrewster that your Half Cent is a 1808 and not a 1802. It is not a question of looking at the date always, which does look like an 8 but imagination can make a 2, but look at other features and the reverse side is all telling that it is not the reverse of an 1802 but matches the 1808 reverse, especially look at the fraction numbers spacing and size.
Congratulations on getting your first Half Cent and may some more be in your future.
Don