Express $0.6 + 0.\overline{7} + 0.4\overline{7}$ in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$.

For each question,select the proper option from four options given,to make the statement true: $\frac{\sqrt{50}}{\sqrt{98}}$ is a $\ldots \ldots \ldots$ number.

Insert a rational number and an irrational number between the following:
$0.15$ and $0.16$

Find five rational numbers between $1$ and $2$.

For each question,select the proper option from four options given,to make the statement true: $\sqrt{5^{2}+12^{2}}$ is a / an $\ldots \ldots$ number.

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.