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) \frac{23}{8} (ii) \frac{125}{441} (iii) \frac{35}{50} (iv) \frac{77}{210} (v) \frac{129}{2^{2} \times 5^{7} \times 7^{17}} \textrm{ }

Foundation

Mathematics Foundation

Properties of Real Number

Recurring Decimal Number

Rational Numbers

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.

(i)

\frac{23}{8}

(ii)

\frac{125}{441}

(iii)

\frac{35}{50}

(iv)

\frac{77}{210}

(v)

\frac{129}{2^{2} \times 5^{7} \times 7^{17}}

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1)

Denominator is

8

,so the rational has a non-terminating decimal expansion

2)

Denominator is a multiple of

3, 7

so the rational number has a terminating decimal expansion

3) \frac{35}{50} = \frac{7}{10}

Denominator is

10

,so the rational has a non-terminating decimal expansion

4) \frac{77}{210} = \frac{11}{30}

Denominator is a multiple of

3

,so the rational has a terminating decimal expansion

5)

Denominator is a multiple of

7

,so the rational has a terminating decimal expansion