Good C Coding practice/etiquette for integrity checks

Two part question;

I'm Coming from a high level Language, so this is a question about form not function;

I've written an isnumeric() function that takes a char[] and returns 1 if the string is a number taking advantage of the isdigit() function in ctype. Similar functions are builtin to other languages and I have always used something like that to integrity check the data before converting it to a numeric type. Mostly because some languages conversion functions fail badly if you try to convert a non-number string to an integer.

But it seems like a kludge having to do all that looping to compensate for the lack of strings in C, which poses the first part of the question;

Is it acceptable practice in C to trap for a 0 return from atoi() in lieu of doing an integrity check on the data before calling atoi()? The way atoi() (and other ascii to xx functions) works seems to lend itself well to eliminating the integrity check altogether. It would certainly seem more efficient to just skip the check.

The second part of the question is; Is there a C function or common library function for a numeric integrity check on a string? (by string, I of course mean char[])