Q. 1 B4.0( 2 Votes )

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


Answer :

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


3 = 3 × 1


8 = 2 × 2 × 2


3 and 8 have no common factors


Therefore, 3 and 8 are co-prime.


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


8 = 23


= 1 × 23


= 50 × 23


So, denominator is of the form 2n5m where n = 3 and m = 0


Thus, is a terminating decimal.


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