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

Asked by Vishal kumar | 2 years ago |  283

1 Answer

Solution :-

Let us we take the examples \( \frac{5}{2}, \frac{5}{4}, \frac{2}{5}, \frac{2}{10}, \frac{5}{16}\) of  the form \( \frac{p}{q}\) that are terminating decimals.

\( \frac{5}{2}\) = 2.5

\( \frac{5}{4}\) = 1.25

\( \frac{2}{5}=0.4\)

\( \frac{2}{10}=0.2\)

\( \frac{5}{16}=0.3125\)

We can observe that the denominators of the above rational numbers have powers of 2, 5 or both. Therefore, q must satisfy in the form either \( 2^m\) or \( 5^n\) or both \( 2^m\times 5^n\) (where m = 0, 1, 2, 3....... and n = 0, 1, 2, 3......) in \( \frac{p}{q}\) form.

Answered by Shivani Kumari | 2 years ago

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