Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:
(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

Question

Philoid · Accepted Answer

Hence we can see that the denominator is of the form 2^m × 5ⁿ and hence decimal expansion of 15/1600 is of terminating type.

Hence we can see that the denominator is of the form 2^m × 5ⁿ and hence decimal expansion of 13/3125 is of terminating type.

Hence we can see that the denominator is of the form 2^m × 5ⁿ and hence decimal expansion of 23/200 is of terminating type.

Hence we can see that the denominator is not of the form 2^m × 5ⁿ and hence decimal expansion of 17/6 is of non-terminating type.

Hence we can see that the denominator is not of the form 2^m × 5ⁿ and hence decimal expansion of 129 / (2² × 5⁷ × 7⁵) is of non-terminating type.

Hence we can see that the denominator is of the form 2^m × 5ⁿ and hence decimal expansion of 35/50 is of terminating type.

Hence we can see that the denominator is of the form 2^m × 5ⁿ and hence decimal expansion of 7/80 is of terminating type.

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:(i) (ii) (iii) (iv) (v) (vi) (vii)