Comparing and ordering decimal numbers

Compare the whole numbers first

To compare two decimal numbers, we look at the whole number part first. The number with the larger whole number part is the larger of the two.

Example: 8.12 < 9.01 because 8 < 9 (regardless of what comes after the decimal point).

If the whole number parts are equal

We then compare the digits after the decimal point, one by one, from left to right (tenths, then hundredths, then thousandths...).

Example: let’s compare 6.48 and 6.5

• Same whole number part: 6 = 6
• Tenths: 4 versus 5 -> 5 is larger
• Therefore 6.5 > 6.48

Useful tip: to make comparison easier, pad with zeros so that both numbers have the same number of decimal places. 6.5 becomes 6.50, and it is clear that 6.50 > 6.48.

Ordering numbers

To order 3.7; 3.07; 3.72; 3.2 in ascending order (from smallest to largest), first convert all the numbers to have the same number of decimal places: 3.70; 3.07; 3.72; 3.20. We then compare the hundredths: 07 < 20 < 70 < 72.

Ascending order: 3.07 < 3.2 < 3.7 < 3.72

A common pitfall to avoid

Never compare the decimal parts as if they were whole numbers! 3.7 is not smaller than 3.72 simply because “7 < 72”: you must always pad with zeros (3.70 and 3.72) before comparing, otherwise you will make a mistake.