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If the Rational Number `A/B`Has a Terminating Decimal Expansion, What is the Condition to Be Satisfied by B? - Mathematics

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Question

If the rational number `a/b`has a terminating decimal expansion, what is the condition to be satisfied by b?

Solution

Let x be a rational number whose decimal expansion terminates.
Then, we can express x in the form `a/b`, where a and b are coprime, and prime factorization
of b is of the form (2m × 5n), where m and n are non-negative integers. 

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Chapter 1: Real Numbers - Exercises 5

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RS Aggarwal Mathematics [English] Class 10
Chapter 1 Real Numbers
Exercises 5 | Q 9

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