Write down the decimal expansions of the rational numbers which have terminating decimal expansions.
(i) $\frac{13}{3125}$ (ii) $\frac{17}{8}$ (iii) $\frac{15}{1600}$ (iv) $\frac{23}{2^{3} 5^{2}}$ (v) $\frac{6}{15}$ (vi) $\frac{35}{50}$

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Solution

The division of all the numbers is shown in figure.

i) $\frac{13}{3125} = 0.00416$

ii) $\frac{17}{8} = 2.125$

iii) $\frac{15}{1600} = 0.009375$

iv) $\frac{23}{2^{3} 5^{2}} = \frac{23}{200} = 0.115$

v) $\frac{6}{15} = 0.4$

vi) $\frac{35}{50} = 0.70$

Here, all the decimal expansions are terminating.

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Question 2
Write down the decimal expansions of
(i) $\frac{13}{3125}$
(ii) $\frac{17}{8}$
(iii) $\frac{15}{1600}$
(iv) $\frac{23}{2^{3} 5^{2}}$
(v) $\frac{6}{15}$
(vi) $\frac{35}{50}$

Q. 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{13}{3125}

(ii)

\frac{17}{8}

(iii)

\frac{64}{455}

(iv)

\frac{15}{1600}

(v)

\frac{29}{343}

(vi)

\frac{23}{2^{3} 5^{2}}

(vii)

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

(viii)

\frac{6}{15}

(ix)

\frac{35}{50}

(x)

\frac{77}{210}

Question 2
Write down the decimal expansions of
(i) $\frac{13}{3125}$
(ii) $\frac{17}{8}$
(iii) $\frac{15}{1600}$
(iv) $\frac{23}{2^{3} 5^{2}}$
(v) $\frac{6}{15}$
(vi) $\frac{35}{50}$