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 |  272

##### 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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