Show that $0.1 \overline{6}=\frac{1}{6}$

For each question, select the proper option from four options given, to make the statement true : (Final answer only)

$0.3 \overline{6}=$

Find the values of each of the following correct to three places of decimals, rationalising the denominator if needed and taking $\sqrt{2}=1.414$ $\sqrt{3}=1.732$ and $\sqrt{5}=2.236$

$\frac{\sqrt{10}-\sqrt{5}}{2}$

Multiply $5 \sqrt{3}$ and $4 \sqrt{12}$.

Insert a rational number and an irrational number between the following:

$0$ and $0.1$

Insert a rational number and an irrational number between the following:

$0.0001$ and $0.001$