Question

Write down the decimal expansions of
(i) $\frac{13}{3125}$
(ii) $\frac{17}{8}$
(iii) $\frac{15}{1600}$

Answer 1

The numbers that had terminating decimal expansions were

(i)
$\frac{13}{3125}=\frac{13}{5^5}=\frac{13\times 2^5}{5^5\times 2^5}=\frac{416}{{10}^5}=0.00416$

(ii)
$\frac{17}{8}=\frac{17}{2^3}=\frac{17\times 5^3}{2^3\times 5^3}=17\times \frac{5^3}{{10}^3}=\frac{2125}{{10}^3}=2.125$

(iii)
$\frac{15}{1600}=\frac{15}{2^4\times {10}^2}=\frac{15\times 5^4}{2^4\times 5^4\times {10}^2}=\frac{9375}{{10}^6}=0.009375$