I've never been compelled to use any fractional approximation of pi. Either I'm doing it in my head and pi is ~3, I'm doing it on paper and pi is ~3.14, or I'm using a calculator and pi is as many digits as I feel like.

We already have the decimal representation memorized for more digits than this approximates, so unless your diameter is given to you in 113ths, is there any practical application here?