Mathematics

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

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Suppose, $\dfrac{p}{q}$ = $\dfrac{2}{5}$ = 0.4

$\dfrac{9}{10}$ = 0.9

$\dfrac{3}{2}$ = 1.5

q must contain factors of 2 or 5 or both.

For example,

In $\dfrac{7}{8}$ , 8 = 2 x 2 x 2

and

in $\dfrac{7}{10}$ , 10 = 2 x 5

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