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:
The denominator is of the form 5m.
Hence, the decimal expansion ofis terminating.
The denominator is of the form 2m.
Hence, the decimal expansion of is terminating.
455 = 5 × 7 × 13
Since the denominator is not in the form 2m × 5n, and it also contains 7 and 13 as its factors, its decimal expansion will be non-terminating repeating.
1600 = 26 × 5…
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