Question 1 (i) - 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: 13/3125 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 13 & 3125 have no common factors, So, 13 & 3125 are co-prime For Denominator (3125) Denominator = 55 = 1 × 55 = 20 × 55 So , denominator is of the form 2n 5m where n = 0 , m = 5 Thus , 13/3125 is a terminating decimal Thus, 64/455 has a non-terminating repeating decimal expansion