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
๐/๐ 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 ร 55
= 20 ร 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

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.