Rational Numbers on a Number Line

Rational Number on a number line:

Let us represent the number ${\displaystyle -\frac{3}{2}}$ on the number line.

• The points to the right of 0 are denoted by + sign and are positive integers. The points to the left of 0 are denoted by – sign and are negative integers.
• Being a negative rational number, it would be marked to the left of 0.
• You know that while marking integers on the number line, successive integers are marked at equal intervals. Also, from 0, the pair 1 and – 1 is equidistant. So are the pairs 2 and -2, 3 and -3.
• In the same way, the rational numbers ${\displaystyle \frac{3}{2}\text{and}-\frac{3}{2}}$ would be at equal distance from 0.
• We know how to mark ${\displaystyle -\frac{3}{2}}$ on the number line. It is marked on the left of 0 and lies halfway between 1 and 2.
• Let us now mark ${\displaystyle \frac{3}{2}}$ on the number line. It lies on the Right of 0 and is at the same distance as ${\displaystyle -\frac{3}{2}}$ from 0.
• In decreasing order, we have, ${\displaystyle \frac{-1}{2},\frac{-2}{2}(=-1),\frac{-3}{2},\frac{-4}{2}(=2)}$.
• This shows ${\displaystyle \frac{-3}{2}}$ lies between – 1 and -2.