Comparing decimals place by place

The idea

Decimals are compared as whole numbers are: start with the digits at the highest place value and move to smaller place values until the digits differ; the number with the larger digit there is greater.

Which is larger?

Which is larger: 6.456 or 6.465?

What do you think?

• 6.456 is larger
• 6.465 is larger
• They are equal

Scan from the left

Start at the highest place. At each place choose: same, or which number has the bigger digit.

The first difference decides

For 6.456 and 6.465, we scan from the left:

So 6.465 is greater than 6.456.

Decimals are compared like whole numbers: start with the highest place value and move to smaller places until the digits differ. The number with the larger digit at that place is greater.

• Place | Digits
• units | 6 and 6: same
• tenths | 4 and 4: same
• hundredths | 5 and 6: different, and 6 is bigger

Notes

To compare decimals, start at the highest place and move right until the digits differ. The larger digit there makes the greater number.

Check yourself

Which is greater: 0.9 or 0.85?

Which is the greatest: 0.5, 0.45, 0.405 or 0.054?

Which of 0.9, 1.1, 1.01 and 1.11 is closest to 1?

Choose the right sign: 4.08 _ 4.8

• 0.9 — correct. Yes! In the tenths place 9 is bigger than 8. We need not look further.
• 0.85. It has more digits, but more digits do not make a number bigger. Compare the tenths: 8 against 9.
• They are equal. 0.9 = 0.90, and 0.90 is more than 0.85.
• 0.054. Its tenths digit is 0, the smallest.
• 0.405. Its tenths digit is 4, less than the 5 in 0.5.
• 0.45. Its tenths digit is 4, less than the 5 in 0.5.
• 0.5 — correct. Yes! Its tenths digit 5 is the biggest of all four.
• 0.9. 0.9 is 10 hundredths away from 1. 1.01 is only 1 hundredth away.
• 1.01 — correct. Yes! 1.01 is only 1 hundredth away from 1. 0.9 and 1.1 are 10 hundredths away, and 1.11 is 11.
• 1.1. 1.1 is 10 hundredths away from 1. 1.01 is only 1 hundredth away.
• 1.11. 1.11 is 11 hundredths away from 1.
• < — correct. Yes! The units are the same. In the tenths place 0 is less than 8.
• >. In the tenths place 0 is less than 8, so 4.08 is the smaller number.
• =. They are different: 4.08 has 0 tenths, 4.8 has 8 tenths.