Work through the examples below, then open Decimals Quiz to check your own numbers and practice the skill.
Align decimal points first
Write the numbers with their decimal points in one vertical column. Compare the whole-number parts first, then tenths, hundredths, thousandths and so on. You may append trailing zeros temporarily to help compare values: 0.7 is the same as 0.70.
For instance, compare 2.405 and 2.45. Both have a whole-number part of 2. Their tenths match at 4, but the hundredths are 0 and 5. Therefore 2.405 < 2.45.
Comparison chart
| Numbers | Correct comparison | Reason |
|---|---|---|
| 0.7 and 0.65 | 0.7 > 0.65 | 0.70 > 0.65 |
| 0.08 and 0.8 | 0.08 < 0.8 | 8 hundredths < 8 tenths |
| 1.250 and 1.25 | Equal | Trailing zero changes nothing |
| −0.2 and −0.9 | −0.2 > −0.9 | Closer to zero |
How to put decimals in order
To sort 0.4, 0.035, 0.45, 0.305, pad to three decimal places: 0.400, 0.035, 0.450, 0.305. From least to greatest, the order is 0.035, 0.305, 0.4, 0.45.
The number of digits after the decimal does not indicate size by itself. Comparing 0.4 and 0.305 as if “305” must be bigger than “4” is a frequent mistake.
Using a number line and negative values
On a number line, values increase to the right. Between 0 and 1, 0.25 sits at one quarter and 0.75 at three quarters. If the numbers are negative, the order reverses relative to their positive distances: −0.8 < −0.3.
This also matters in temperatures and accounting. A change of −0.5 is a greater drop than a change of −0.05.
Practice: order four numbers
Arrange 1.09, 1.9, 1.099, 1.01 from least to greatest. Then decide whether 0.005 is greater than 0.05.
Answers: 1.01, 1.09, 1.099, 1.9. And 0.005 < 0.05 because 5 thousandths is smaller than 5 hundredths.
Fast checking method
Write each number to the same decimal length if needed, compare positions and verify with a number line. Use the Decimals Quiz for additional varied questions; the place-value chart provides explanations if two numbers still look confusing.
Frequently asked questions
Is 0.7 greater than 0.65?
Yes. 0.7 = 0.70, and 70 hundredths is greater than 65 hundredths.
Is 0.50 equal to 0.5?
Yes. A trailing zero after the decimal does not change the value.
Which is greater: −0.4 or −0.6?
−0.4 is greater because it lies closer to zero on the negative side of the number line.
Use Decimals Quiz to verify a new example, then try the related practice activities.