# Rational Number on a number line:

Let us represent the number -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 3/2 "and" -3/2 would be at equal distance from 0.
• We know how to mark -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 3/2 on the number line. It lies on the Right of 0 and is at the same distance as -3/2 from 0.
• In decreasing order, we have, (-1)/2, (-2)/2 (= -1), (-3)/2, (-4)/2 (= 2).
• This shows (-3)/2 lies between – 1 and -2.

#### Example

Show the following numbers on a number line.

7/3, 2, (-2)/3

Steps:

1. Let us draw a number line.
2. We can show the number 2 on a number line.
3. 7/3 = 7 xx 1/3, therefore each unit on the right side of zero is to be divided in three equal parts. The seventh point from zero shows 7/3; or 7/3 = 2 + 1/3, hence the point at 1/3"rd distance of unit after 2 shows" 7/3.
4. To show (-2)/3 on the number line, first, we show 2/3 on it. The number to the left of 0 at the same distance will show the number (-2)/3.
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How to Represent Rational Numbers on a Number Line? [00:18:56]
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