Question

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) $\frac{35}{50}$

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

(iv) $\frac{23}{2^3{5}^2}=\frac{23}{2^3{5}^2}\times \frac{5}{5}=\frac{23\times 5}{2^3{5}^3}=\frac{115}{{10}^3}=0.115$

(v) $\frac{6}{15}=\frac{2}{5}=\frac{2\times 2}{5\times 2}=\frac{4}{10}=0.4$

(vi) $\frac{35}{50}=\frac{7}{10}=0.7$