Question

Look at several examples of rational numbers in the form 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?

Answer 1

Solution: If the denominator is product of 2 and 5 only then it will always give terminating number For example 7/2 = 0.35, 19/10 = 1.9, 12/5 = 2.5, 1/25 = 0.04, 1/ 4 = 0.25 and you can write such many examples.

Answer 2

$\huge \underline \mathbb {SOLUTION:-}$

We observe that when q is 2, 4, 5, 8, 10… Then the decimal expansion is terminating. For example:

1/2 = 0. 5, denominator q = 2¹

7/8 = 0. 875, denominator q =2³

4/5 = 0. 8, denominator q = 5¹

We can observe that the terminating decimal may be obtained in the situation where prime factorization of the denominator of the given fractions has the power of only 2 or only 5 or both.