Find three rational numbers between:

2 and 3

Write both the numbers with a common denominator, then multiply the numerator and the denominator of each by one more than the number of rational numbers required.

To insert 3 rational numbers between 2 and 3, multiply both the numerator and the denominator of each number by 3 + 1 i.e. 4.

$\Rightarrow 2 = \dfrac{2 \times 4}{1 \times 4} = \dfrac{8}{4} \\[1em] \Rightarrow 3 = \dfrac{3 \times 4}{1 \times 4} = \dfrac{12}{4}$

As 8 < 9 < 10 < 11 < 12,

$\therefore \dfrac{8}{4} \lt \dfrac{9}{4} \lt \dfrac{10}{4} \lt \dfrac{11}{4} \lt \dfrac{12}{4}$

Hence, three rational numbers between 2 and 3 are $\mathbf{\dfrac{9}{4}, \dfrac{10}{4} \text{ and } \dfrac{11}{4}}$.