# Real Numbers

#### Question 1:

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:

(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}^{ }× 5^{n}, and it also contains 7 and 13 as its factors, its decimal expansion will be non-terminating repeating.

(iv)** **

1600 = 2^{6} ×...

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