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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? Q.6

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Today i am solving the important question of ncert class 9th chapter 1.3 question number 6 how is solve this tricky question easily and fast . Sir please help me to solve this question in easy way and give me the best solution of this 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?

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  1. 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.

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