Q. 1 C5.0( 2 Votes )

# 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

29 = 29 × 1

343 = 7 × 7 × 7

29 and 343 have no common factors

Therefore, 29 and 343 are co-prime.

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

343 = 73

So, denominator is not of the form 2n5m

Thus, is a non-terminating repeating decimal.

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