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 (expansions). Can you guess what property q must satisfy?

Solution:

Terminating decimal expansion will occur when denominator $q$ of rational number $\frac{p}{q}$ is either of $2,4,5,8,10$, and so on...

$\frac{9}{4}=2.25$

$\frac{11}{8}=1.375$

$\frac{27}{5}=5.4$

It can be observed that terminating decimal may be obtained in the situation where prime factorisation of the denominator of the given fractions has the power of 2 only or 5 only or both.