    Question

# Which of the following have a non terminating decimal expansion?

A

77/210

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B

23/8

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C

17/80

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D

35/50

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Solution

## The correct options are A 77/210 B 23/8 If pq is a rational number with terminating decimal expansion where p and q are coprimes, then the prime factorisation of q will be in the form of 2n5m, where n and m are non - negative integers. Consider the fraction 17210. Here 210 = 2 × 3 × 5 ×7 Hence 210 is not in the form of 2n5m. Consider the fraction 239. Here 9 = 3 × 3 = 32 Hence 9 is not in the form of 2n5m. Consider the fraction 1780. Here 80 = 2 × 2 × 2 × 2 × 5 = 24×5 Hence 80 is in the form of 2n5m with n = 4 and m = 1. Consider the fraction 3550=710. Here 10 = 2 × 5 = 21×51 Hence 10 is in the form of 2n5m with n = 1 and m = 1. Therefore, 17210 and 239 will have non - terminating decimal expansion.  Suggest Corrections  2      Similar questions  Related Videos   Condition of Terminating/Non Terminating Recurring Decimal Expansion
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