Which decimal is bigger?
When you compare decimals, the number of digits doesn’t tell you the size. 0.8 is bigger than 0.75, even though 0.75 has more digits. You need place value.
The method
- Line up the decimals by their decimal points.
- Add trailing zeros so they have the same number of decimal places.
- Compare digits from left to right, place by place.
- The first place where the digits differ decides which is bigger.
Example: Compare 0.8 and 0.75.
| Ones | . | Tenths | Hundredths | |
|---|---|---|---|---|
| 0.80 | 0 | . | 8 | 0 |
| 0.75 | 0 | . | 7 | 5 |
Ones are the same (0). Tenths: 8 > 7. So 0.8 > 0.75.
Why trailing zeros help
0.8 = 0.80 because 8 tenths = 80 hundredths. Writing both numbers to hundredths lets you compare 80 and 75 as if they were whole numbers.
Ordering decimals
Example: Order 2.3, 2.03, 2.33, 2.303 from least to greatest.
| Number | Written to thousandths |
|---|---|
| 2.3 | 2.300 |
| 2.03 | 2.030 |
| 2.33 | 2.330 |
| 2.303 | 2.303 |
All have 2 ones. Compare tenths: 2.030 has 0 tenths, so it’s smallest. The others have 3 tenths; compare hundredths: 2.300 and 2.303 have 0; 2.330 has 3. Then thousandths: 2.300 < 2.303.
Order: 2.03, 2.3, 2.303, 2.33.
Using a number line
Place the decimals on a number line. The one furthest right is the greatest. Zooming in (from 0 to 1, then 0.7 to 0.8) shows tiny differences clearly.
Money check
Think of decimals as money: $0.80 vs $0.75. Eighty cents is more than seventy-five cents.
Worked examples
Example 1: Which is greater: 4.09 or 4.1?
4.09 vs 4.10. Tenths: 0 < 1. 4.1 is greater.
Example 2: Order 0.5, 0.45, 0.405 from greatest to least.
0.500, 0.450, 0.405 → 0.5, 0.45, 0.405.
Example 3: Fill in >, < or =: 3.60 ◯ 3.6
Trailing zero changes nothing: =.
Common mistakes
- Thinking longer decimals are bigger: 0.123 < 0.2.
- Not lining up the decimal points.
- Comparing as whole numbers: thinking 0.45 > 0.5 because 45 > 5.
Try it yourself
- 0.6 ◯ 0.59
- 7.08 ◯ 7.8
- 1.250 ◯ 1.25
- Order from least to greatest: 0.3, 0.33, 0.303.
- Order from greatest to least: 5.1, 5.01, 5.11.
Answers: 1) > 2) < 3) = 4) 0.3, 0.303, 0.33 5) 5.11, 5.1, 5.01
Quick recap
- Line up decimal points and add trailing zeros.
- Compare place by place from the left.
- More digits doesn’t mean a bigger number.