Look at several examples of rational numbers in the form ( q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating, decimal representations. Can you guess what property q must satisfy?

Question

Look at several examples of rational numbers in the form ( q &#x2260; 0), where p and q are integers with no common factors other than 1 and having terminating, decimal representations. Can you guess what property q must satisfy?

Philoid · Accepted Answer

A rational number is a terminating decimal only, when prime factors of q are 2 and 5 only. Therefore, is a terminating decimal only, when prime factorisation of q must have only powers of 2 or 5 or both.

Look at several examples of rational numbers in the form (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating, decimal representations. Can you guess what property q must satisfy?