atoi — how to identify the difference between zero and error?

http://www.cplusplus.com/reference/clibrary/cstdlib/atoi/

Return Value

On success, the function returns the converted integral number as an int value. If no valid conversion could be performed, a zero value is returned. If the correct value is out of the range of representable values, INT_MAX or INT_MIN is returned.

So how I differ between atoi("poop") and atoi("0") and atoi("0000000")

Yes I can loop and check for all zeroes in case I get 0 result, but isn't there a better way?

Notice: I use ANSI C89