Question 1 (vi) - 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: (vi) 23/(23 52) 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 23 & 23 52 have no common factors, So, 23 & 23 52 are co-prime For Denominator (23 52 ) Denominator = 23 × 52 So , denominator is of the form 2n 5m where n = 3 , m = 2 Thus , 23/(23 52) is a terminating decimal