Insert three rational numbers between 4 and 4.5.

A rational number between 4 and 4.5

$= \dfrac{4 + 4.5}{2} \\[0.5em] = \dfrac{8.5}{2} \\[0.5em] = \bold{4.25} \\[0.5em]$

A rational number between 4 and 4.25

$= \dfrac{4 + 4.25}{2} \\[0.5em] = \dfrac{8.25}{2} \\[0.5em] = \bold{4.125} \\[0.5em]$

A rational number between 4 and 4.125

$= \dfrac{4 + 4.125}{2} \\[0.5em] = \dfrac{8.125}{2} \\[0.5em] = \bold{4.0625} \\[0.5em]$

As, 4 < 4.0625 < 4.125 < 4.25 < 4.5, therefore three rational numbers between 4 and 4.5 are 4.0625, 4.125, 4.25.