Question

If the rational number $\frac{a}{b}$ has a terminating decimal expansion, what is the condition to be satisfied by b?

Answer 1

Let x be a rational number whose decimal expansion terminates.
Then, we can express x in the form $\frac{a}{b}$, where a and b are coprime, and prime factorization of b is of the form (2^m × 5ⁿ), where m and n are non negative integers.