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?
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 and Explanation
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.
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