Convert following rational numbers in decimal form and state the kind of its decimal expansion

$\frac{4}{13}$

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

$0.2555 \ldots$

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

$0.404040 \ldots$

Rationalise the denominator in each of the following

$\frac{1}{7-4 \sqrt{3}}$

State whether the following statements are true or false? Justify your answer.

$(i)$ $\frac{\sqrt{2}}{3}$ is a rational number.

$(ii)$ There are infinitely many integers between any two integers.

State whether the following statements are true or false

Every whole number is an integer.