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

Transcript

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: (ii) 17/8 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 17 & 8 have no common factors, So, 17 & 8 are co-prime For Denominator (8) Denominator = 23 = 1 × 23 = 50 × 23 So , denominator is of the form 2n 5m where n = 3 , m = 0 Thus, 17/8 is a terminating decimal