Question Statement :

Comment on the following statements:

Statement A: Let x be a rational number whose decimal expansion terminates. Then x can be expressed in $\genfrac{}{}{0.1ex}{}{p}{q}$, where p and q are co-prime, and the prime factorisation of q is of the form $2^n\cdot 5^m$, where n, m are non-negative integers.

Statement B: Let $x=\genfrac{}{}{0.1ex}{}{p}{q}$ be a rational number such that prime factorization of q is not of the form $2^n\cdot 5^m$ where n, m are non-negative integers, and p and q are co-prime. Then x has a decimal expansion which is non-terminating and repeating.