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

$0.1 \overline{134}$

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

$0$ and $0.1$

Fill in the blanks so as to make each of the following statements true (Final answer only)

$\sqrt{1 \frac{25}{144}}=\ldots \ldots$

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

$(i)$ Number of rational numbers between $15$ and $18$ is finite.

$(ii)$ There are numbers which cannot be written in the form $\frac{p}{q}, q \neq 0, p , q$ both are integers.

Let $x$ and $y$ be rational and irrational numbers, respectively. Is $x+y$ necessarily an irrational number? Give an example in support of your answer.

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

$\frac{\sqrt{15}}{\sqrt{3}}$ is written in the form $\frac{p}{q},$ where $q \neq 0$ so it is a rational number.