Question 1 Write whether the rational number 7/75 will have a terminating decimal expansion or a nor-terminating repeating decimal expansion. Theory
/ 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
7/75
Checking co-prime
7 & 75 have no common factors,
So, 7 & 75 are co-prime
For Denominator (75)
Denominator = 3 52
So , denominator is not of the form 2n 5m
Thus , 7/75 is a non-terminating repeating decimal expansion
Hence 75 = 3 5 5
= 3 52

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.