For each question,select the proper option from the four options given to make the statement true: $0.\overline{3} = \dots$

Rationalise the denominator of the following expression and evaluate it by taking $\sqrt{3} = 1.732$,up to three decimal places:
$\frac{4}{\sqrt{3}}$

Find the value of $b$ :
$\frac{\sqrt{2}+\sqrt{3}}{3 \sqrt{2}-2 \sqrt{3}}=2-b \sqrt{6}$

State the type of the decimal expansion of $\frac{1}{7}$.

Simplify the following:
$\frac{3}{\sqrt{8}} + \frac{1}{\sqrt{2}}$

Find the value of the following expression correct to three decimal places,rationalizing the denominator if needed. Take $\sqrt{2} = 1.414$,$\sqrt{3} = 1.732$,and $\sqrt{5} = 2.236$.
$\frac{\sqrt{2}}{2+\sqrt{2}}$