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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? - CBSE Class 9 - Mathematics

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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?

Solution

The property that q must satisfy in order that the rational numbers in the form p/q, where p and q are integers with no common factors other than 1, have terminating decimal representation (expansions) is that the prime factorization of q has only powers of 2 or powers of 5 or both, i.e., q must be of the form 2m x 5n ; m = 0,1,2,3,............,  n = 0,1,2,3,.............

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APPEARS IN

 NCERT Solution for Mathematics Class 9 (2018 to Current)
Chapter 1: Number Systems
Ex. 1.30 | Q: 6 | Page no. 14

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Solution 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? Concept: Real Numbers and Their Decimal Expansions.
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