There exists no value for 0/0.Its one of the indeterminate forms just like infinity/infinty , infinity – infinity , 0 * infinity , 1^ infinity , 0^0 and inifnity ^ 0 are indeterminate forms.
The reason for the ambiguity of 0/0 can be explained ike this,
We know that x/0 is infinity where x is any number.And also we know that x/x is 1.But we also know that 0/x where x is any number is 0.Here we can see that we have 3 different answers for 0/0.Hence its value is not determinable.