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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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