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


64 = 26


455 = 5 × 7 × 13


64 and 455 have no common factors


Therefore, 64 and 455 are co-prime.


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


455 = 5 × 7 × 13


So, denominator is not of the form 2n5m


Thus, is a non-terminating repeating decimal.


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

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