Look at several examples of rational numbers in the form \(\frac{p}{q}\) (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?

Look at several examples of rational numbers in the form \(\frac{p}{q

1.	Look at several examples of rational numbers in the form \(\frac{p}{q}\) (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?
Answer» A rational number \(\frac{p}q\) is a terminating decimal only, when prime factors of q are 2 and 5 only. Therefore, \(\frac{p}q\) is a terminating decimal only, when prime factorisation of q must have only powers of 2 or 5 or both.