Insert a rational number and an irrational number between $2$ and $3$.

State whether the following statements are true or false. Justify your answer.
$(i)$ The number of rational numbers between $15$ and $18$ is finite.
$(ii)$ There are numbers which cannot be written in the form $\frac{p}{q}$,where $q \neq 0$ and $p, q$ are both integers.

State whether the following statement is true or false:
Each integer is a whole number.

Represent $\sqrt{8.1}$ geometrically on the number line.

Classify the following numbers as rational or irrational:
$(i)$ $\sqrt{23}$
$(ii)$ $\sqrt{225}$
$(iii)$ $0.3796$
$(iv)$ $7.478478 \ldots$
$(v)$ $1.101001000100001 \ldots$

Insert a rational number and an irrational number between the following:
$0.0001$ and $0.001$