Look at several examples of rational number in the form $\frac{p}{q}$ $(q \neq 0)$ , 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 ?

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Solution

The property is if the denominators have factors 2 or 5 or both, the decimal representation will be terminating

E.g.

$\frac{1}{2}$ = 0.5, $\frac{1}{4}$ = 0.25, $\frac{1}{5}$ = 0.2,

$\frac{1}{10}$ = 0.1, $\frac{1}{20}$ = 0.5, $\frac{3}{8}$ = 0.125,

$\frac{3}{40}$ = 0.075 etc.

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Look at several examples of rational number in the form $\frac{p}{q}$ $(q \neq 0)$ , 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 ?

The property is if the denominators have factors 2 or 5 or both, the decimal representation will be terminating

E.g.

$\frac{1}{2}$ = 0.5, $\frac{1}{4}$ = 0.25, $\frac{1}{5}$ = 0.2,

$\frac{1}{10}$ = 0.1, $\frac{1}{20}$ = 0.5, $\frac{3}{8}$ = 0.125,

$\frac{3}{40}$ = 0.075 etc.