Write down the decimal expansions of those rational numbers in Question

Question.

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

Solution:

(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}}$$=\frac{17 \times 5^{3}}{\mathbf{2}^{3} \times \mathbf{5}^{3}}=\frac{\mathbf{1 7} \times \mathbf{5}^{3}}{\mathbf{1 0}^{3}}=\frac{\mathbf{2 1 2 5}}{\mathbf{1 0}^{3}}=2.125 (iv) \frac{15}{1600}=\frac{15}{2^{6} \times 5^{2}}=\frac{3 \times 5}{2^{6} \times 5^{2}}=\frac{3}{2^{6} \times 5}$$=0.009375$

(vi) $\frac{\mathbf{2 3}}{\mathbf{z}^{3} \times \mathbf{5}^{\mathbf{2}}}=0.115$

(viii) $\frac{\mathbf{6}}{\mathbf{1 5}}=\frac{\mathbf{2} \times \mathbf{3}}{\mathbf{3} \times \mathbf{5}}=\frac{\mathbf{2}}{\mathbf{5}}=0.4$

(ix) $\frac{\mathbf{3 5}}{\mathbf{5 0}}=\frac{\mathbf{5} \times \mathbf{7}}{\mathbf{2} \times \mathbf{5}^{\mathbf{2}}}=\frac{\mathbf{7}}{\mathbf{2} \times \mathbf{5}}=0.7$