Question

Express $3.\overline{8}$ in the $\frac{p}{q}$ form

Answer 1

Let $x=3.\overline{8}=3.8888$ ..................(1)

Multiplying (1) by $10$, we get:

$10x=38.8888$ .................(2)

Now, on subtracting (1) from (2), we get:

$9x=35$

$\Rightarrow x=\frac{9}{35}$

Hence, $3.\overline{8}=\frac{35}{9}$.