Write three numbers whose decimal expansions are non-terminating non-recurring.

Find an irrational number between $\frac{1}{7}$ and $\frac{2}{7}$. (in $...$)

Show that $0.3333... = 0.\overline{3}$ can be expressed in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \ne 0$.

Are the square roots of all positive integers irrational? If not,give an example of the square root of a number that is a rational number.

State whether the following statements are true or false. Justify your answers.
$(i)$ Every irrational number is a real number.
$(ii)$ Every point on the number line is of the form $\sqrt{m}$,where $m$ is a natural number.
$(iii)$ Every real number is an irrational number.

Show that $1.272727 \ldots = 1.\overline{27}$ can be expressed in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \neq 0$.