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

$0 . \overline{001}$

State whether the following statements are true or false

Every whole number is a rational number.

Every rational number is

Rationalise the denominator of the following:

$\frac{4 \sqrt{3}+5 \sqrt{2}}{\sqrt{48}+\sqrt{18}}$

State whether each of the following statements is true or false

Each integer is a whole number.

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

$\frac{1}{3}$ and $\frac{1}{2}$