Question

Convert into vulgar fraction:
$0.\overline{37}$

Answer 1

Step: Convert into a vulgar fraction

Given: $0.3\overline{7}$

$\Rightarrow 0.3\overline{7}=\mathrm{0.3777...}$

Here, 7 is the only digit that is repeating in the decimal part.

$\Rightarrow 0.3\overline{7}$

$=\frac{37-3}{90}$

$=\frac{34}{90}$

$=\frac{34÷2}{90÷2}$

$=\frac{17}{45}$

$\therefore 0.3\overline{7}=\frac{17}{45}$