Express $0.\overline{83}$ in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.

Simplify the following expression: $(3+\sqrt{5})(4-\sqrt{11})$

Rationalise the denominator of the following: $\frac{\sqrt{40}}{\sqrt{3}}$

Rationalise the denominator of the following:
$\frac{\sqrt{6}}{\sqrt{2}+\sqrt{3}}$

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 $\sqrt{5} = 2.236$.
$\frac{\sqrt{2}}{2+\sqrt{2}}$

Represent the following numbers on the number line:
$7, 7.2, \frac{-3}{2}, \frac{-12}{5}$