Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0.888 \ldots$

Simplify the following:
$4 \sqrt{28} \div 3 \sqrt{7}$

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

Rationalise the denominator in each of the following and hence evaluate by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ up to three decimal places.
$\frac{\sqrt{10}-\sqrt{5}}{2}$

If $\frac{5+3 \sqrt{3}}{7+4 \sqrt{3}}=a+b \sqrt{3},$ find the value of $a$ and $b$.

Find three rational numbers between $\frac{1}{4}$ and $\frac{1}{5}$.