Write down the decimal expansions of those rational numbers in Question 1 above
which have terminating decimal expansions.

(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) $\frac{77}{210}$

(i) Since it has a terminating decimal expansion, decimal expansion can be found.

So, $\frac{13}{3125}=0.00416$

(ii) Since it has a terminating decimal expansion, decimal expansion can be found.

So, $\frac{17}{8}=2.125$

(iii) Since it has a non-terminating decimal expansion, decimal expansion cannot be found.

(iv) Since it has a terminating decimal expansion, decimal expansion can be found.

So, $\frac{15}{1600}=0.009375$

(v) Since it has a non-terminating decimal expansion, decimal expansion cannot be found.

(vi) Since it has a terminating decimal expansion, decimal expansion can be found.

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

So, $\frac{23}{2^3 5^2}=0.115$

(vii) Since it has a non-terminating decimal expansion, decimal expansion cannot be found.

(viii) Since it has a terminating decimal expansion, decimal expansion can be found.

$\frac{6}{15}=\frac{2}{5}$

So, $\frac{6}{15}=0.4$

(ix) Since it has a terminating decimal expansion, decimal expansion can be found.

$\frac{35}{50}=\frac{7}{10}$

So, $\frac{35}{50}=0.7$

(x) Since it has a non-terminating decimal expansion, decimal expansion cannot be found.