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
Made by
Davneet Singh
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo
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