it's actually not 0. it's an impossibility if you were to have a test that asked this question there would be an option for not possible and zero, and if you picked zero you would be wrong http://en.wikipedia.org/wiki/Division_by_zero 0/0 is known as an indeterminate form
The answer is undefined. The reason for that is because the problem conflicts with 2 rules. 1) 0 divided by anything is 0. 2) Anything divided by itself is one. Therefore it is undetermined, since no one has stood up and stated what they think the answer is.