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Question

# Which of the following rational numbers is a non-terminating and repeating decimal?

A
3250
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B
1732
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C
725
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D
1736
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Solution

## The correct option is D 1736 A fraction is terminating only when the prime factors of denominator are only 2 and 5. Otherwise, the fraction is non-terminating and repeating. For example: The prime factors of 250, 25 and 32 contain only 2 and 5. 250=2×53Thus, 3250=0.012 is a terminating decimal. 25=20×52,Thus, 725=0.28 is a terminating decimal. 32=25×50Thus, 1732=0.53125 is a terminating decimal. 36=22×32Thus, 1736=0.47222... non-terminating and repeating decimal.

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