Write whether the rational number 7/75 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

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Question 1 Write whether the rational number 7/75 will have a terminating decimal expansion or a nor-terminating repeating decimal expansion. Theory / is terminating if (i) p & q are co-prime and (ii) q is of the form 2n 5m where n & m are non-negative integers 7/75 Checking co-prime 7 & 75 have no common factors, So, 7 & 75 are co-prime For Denominator (75) Denominator = 3 52 So , denominator is not of the form 2n 5m Thus , 7/75 is a non-terminating repeating decimal expansion Hence 75 = 3 5 5 = 3 52

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.