Q1 of 104 Page 1

Without actually performing the long division, state whether the following rational numbers have terminating or non-terminating repeating (recurring) decimal expansion.

Given rational number is


=


is terminating if


a) p and q are co-prime &


b) q is of the form of 2n 5m where n and m are non-negative integers.


Firstly, we check co-prime


7 = 1 × 7


10 = 2 × 5


7 and 10 have no common factor


Therefore, 7 and 10 are co-prime.


Now, we have to check that q is in the form of 2n5m


10 = 51 × 21


So, denominator is of the form 2n5m where n = 1 and m = 1


Thus, is a terminating decimal.


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