Question 1 (iv) - Decimal Expansion - Chapter 1 Class 10 Real Numbers

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Ex 1.4 , 1 Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion: (iv) 15/1600 15/1600 = 3/320 𝑝/𝑞 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 Checking co-prime 3 & 320 have no common factors, So, 3 & 320 are co-prime For Denominator (320) Denominator = 26 × 51 So , denominator is of the form 2n 5m where n = 6 , m = 1 Thus, 3/320 i.e. 15/1600 is a terminating decimal