Question

# Find out two rational numbers between $\dfrac{-3}{4},0.$

Hint:Get the decimal form of the fraction $\dfrac{-3}{4}$ by dividing -3 by 4. Now, write down any two numbers between the given numbers (after converting the fraction $\dfrac{-3}{4}$ to decimal form). Use the following definition of rational number to get the answer.Rational number is a number which can be represented in form of $\dfrac{p}{q}$ , where $q\ne 0$ and p and q are real numbers. It is of terminating or recurring type numbers in decimal form.

First let us understand the definition of rational numbers.
Terminating: The number in decimal form has fixed digits (before the decimal and after decimal both)
Recurring: The numbers which have some repeating digits after the decimal.
Now, coming to the question as we need to find the two rational numbers between $\dfrac{-3}{4},0$ . So, we can represent $\dfrac{-3}{4}$ in decimal form by dividing (-3) by 4. Hence, we get
$\dfrac{-3}{4}=-0.75$
So, we need to find two rational numbers between -0.75 and 0. Hence, we can write any two numbers between -0.75 and 0, which is a rational as per the definition of rational number. So, we can write two rational numbers between -0.75 and 0 as
- 0.50, - 0.35
So, - 0.50 and – 0.35 are two rational between $\dfrac{-3}{4},0$

Note: Another approach to get two rational numbers are x and y can also be given as
$\dfrac{1}{2}\left( x+y \right),\dfrac{1}{3}\left( x+y \right),\dfrac{1}{4}\left( x+4 \right),\dfrac{2}{3}..................etc$
where $x=\dfrac{-3}{4}$ and $y=0$
So, two rational numbers between $\dfrac{-3}{4},0$ can be also given as
$\dfrac{1}{2}\left( \dfrac{-3}{4}+0 \right)=\dfrac{-3}{8},\dfrac{1}{3}\left( \dfrac{-3}{4}+0 \right)=\dfrac{-1}{4}$
Don’t write any irrational number between $\dfrac{-3}{4},0$ . One may go wrong if he or she does not know the definition of irrational numbers. Irrational numbers are non- terminating and non-recurring example:$1.3231456..................\sqrt{3},\sqrt{5}$ ,So be clear with the terminology as well.