Question

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:

Answer 1

(i)

The denominator is of the form 5^m.

Hence, the decimal expansion ofis terminating.

(ii)

The denominator is of the form 2^m.

Hence, the decimal expansion of is terminating.

(iii)

455 = 5 × 7 × 13

Since the denominator is not in the form 2^m × 5ⁿ, and it also contains 7 and 13 as its factors, its decimal expansion will be non-terminating repeating.

(iv)

1600 = 2⁶ × 5²

The denominator is of the form 2^m × 5ⁿ.

Hence, the decimal expansion of is terminating.

(v)

Since the denominator is not in the form 2^m × 5ⁿ, and it has 7 as its factor, the decimal expansion of is non-terminating repeating.

(vi)

The denominator is of the form 2^m × 5ⁿ.

Hence, the decimal expansion of is terminating.

(vii)

Since the denominator is not of the form 2^m × 5ⁿ, and it also has 7 as its factor, the decimal expansion of is non-terminating repeating.

(viii)

The denominator is of the form 5ⁿ.

Hence, the decimal expansion of is terminating.

(ix)

The denominator is of the form 2^m × 5ⁿ.

Hence, the decimal expansion of is terminating.

(x)

Since the denominator is not of the form 2^m × 5ⁿ, and it also has 3 as its factors, the decimal expansion of is non-terminating repeating.