Question

Find two rational numbers between 2 and 3.

Answer 1

Hint: We will multiply and divide a same number greater than 2 to both the given numbers, say 3 as $3 > 2$. When we will multiply and divide by 3, the numbers 2 and 3 will be equivalent to $\dfrac{6}{3}$ and $\dfrac{9}{3}$. Now, we can easily write two rational numbers between 2 and 3.

Complete step-by-step answer:
We have to find two rational numbers between 2 and 3.
Rational numbers are of the form $\dfrac{p}{q},q \ne 0$.
There are infinite rational numbers between any two numbers.
Since, we have to find two rational numbers between 2 and 3, we will multiply and divide a same number greater than 2 to both the given numbers.
Let us multiply these numbers by 3.
$\dfrac{{2 \times 3}}{3} = \dfrac{6}{3}$ and $\dfrac{{3 \times 3}}{3} = \dfrac{9}{3}$
Now, we can easily write two rational numbers between 2 and 3.
That are, $\dfrac{7}{3},\dfrac{8}{3}$
Hence, $\dfrac{7}{3},\dfrac{8}{3}$ are two rational numbers between 2 and 3.

Note: We have multiplied and divided here the numbers by 3, but we can use any number greater than 2. Every whole number has 1 as its denominator, like 3 is equivalent to $\dfrac{3}{1}$. Therefore, we can say every natural number is also a rational number. Also, there are infinite rational numbers between any two numbers. Rational numbers can be plotted on a number line and hence are real numbers.