Question 1 (v) - 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: (v) 29/343 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 29 & 343 have no common factors, So, 29 & 343 are co-prime For Denominator (343) Denominator = 7 × 7 × 7 So , denominator is not of the form 2n 5m Thus, 29/343 has a non-terminating repeating decimal expansion