Question

0.5737373.... is equal to:

• A. $\frac{284}{497}$
• B. $\frac{284}{495}$
• C. $\frac{568}{999}$
• D. $\frac{567}{990}$

Answer 1

Answer: (B)

$\frac{284}{495}$

Let $y=\mathrm{0.5737373.....}=0.5\overline{73}=0.5+\frac{73}{{10}^3}+\frac{73}{{10}^5}+....$

$\Rightarrow y=\frac{1}{2}+\frac{73}{{10}^3}(1+\frac{1}{{10}^2}+\frac{1}{{10}^4}+.....)$

$=\frac{1}{2}+\frac{73}{1000}\cdot \frac{1}{1-\frac{1}{100}}=\frac{1}{2}+\frac{73}{990}=\frac{284}{495}$