Comparing and ordering relative numbers

The number line

To compare relative numbers, we use a number line. We place 0 in the centre: positive numbers are to the right, negative numbers are to the left.

<--|----|----|----|----|----|----|--> -3 -2 -1 0 +1 +2 +3

The further to the right a number is on the number line, the larger it is.

Rules for comparison

1. A positive number is always greater than a negative number: +2 > -100
2. When comparing two positive numbers, we compare them as usual: +3 < +8
3. When comparing two negative numbers, the one that is closer to zero is greater: -2 > -8 (because -2 is closer to zero, and therefore further to the right)

Examples

• Compare -5 and +1 -> +1 > -5
• Compare -10 and -3 -> -10 < -3
• Put the following in ascending order: -7; +2; -1; 0 -> -7 < -1 < 0 < +2

Common pitfall

The most common pitfall: thinking that -8 > -2 because ‘8 is greater than 2’. This is not true for negative numbers! The larger the absolute value of a negative number, the smaller the number itself (the further it is from zero to the left). If in doubt, draw a number line.