Q. 1 H4.0( 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

2 and 5 have no common factor

Therefore, 2 and 5 are co-prime.

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

5 = 51 × 1

= 51 × 20

So, denominator is of the form 2n5m where n = 0 and m = 1

Thus, is a terminating decimal.

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