Question

If the rational number 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.