Why round decimals?
Calculators often show long decimals: 10 ÷ 3 = 3.3333333. Prices, measurements and statistics are usually rounded to a sensible number of decimal places.
The rule
- Find the rounding digit (the place you’re rounding to).
- Look at the digit just to its right.
- If it’s 5 or more, add 1 to the rounding digit.
- If it’s 4 or less, keep the rounding digit.
- Drop all digits to the right.
Examples
| Number | Round to | Rounding digit | Next digit | Result |
|---|---|---|---|---|
| 3.47 | Nearest tenth | 4 | 7 → up | 3.5 |
| 3.42 | Nearest tenth | 4 | 2 → stay | 3.4 |
| 8.365 | Nearest hundredth | 6 | 5 → up | 8.37 |
| 0.0731 | Nearest hundredth | 7 | 3 → stay | 0.07 |
| 12.6 | Nearest whole | 2 | 6 → up | 13 |
When the rounding digit is 9
Rounding up a 9 makes it 10, so carry 1:
- 2.97 to the nearest tenth → 3.0
- 4.996 to the nearest hundredth → 5.00
Keep the trailing zero (3.0, 5.00). It shows how precise the answer is.
Rounding money
Money is usually rounded to the nearest cent (hundredth): $12.678 → $12.68.
Using a number line
3.47 sits between 3.4 and 3.5. Halfway is 3.45. Since 3.47 is past halfway, it rounds to 3.5.
How many places?
Choose a sensible precision for the situation, keeping only the digits that are significant for the job:
| Situation | Typical rounding |
|---|---|
| Money | 2 decimal places |
| Height in metres | 2 decimal places (cm) |
| Batting average | 3 decimal places |
| Race times | 2 decimal places (hundredths of a second) |
| Temperature | 1 decimal place |
Keep extra digits during a calculation and round only the final answer. Rounding too early can make results wrong.
Worked examples
Example 1: Round 6.284 to the nearest hundredth.
Hundredths digit 8; next digit 4 → stay: 6.28.
Example 2: Round 0.95 to the nearest tenth.
Tenths digit 9; next digit 5 → up: 1.0.
Example 3: Round 15.5 to the nearest whole number.
16.
Common mistakes
- Looking at the wrong digit. Look only at the digit right after the rounding place.
- Rounding in a chain: 2.445 → 2.45 → 2.5 is wrong; 2.445 rounded to the nearest tenth is 2.4.
- Dropping needed zeros: 2.97 to the nearest tenth is 3.0, not 3.
- Rounding too early in a multi-step problem.
Try it yourself
- Round 7.26 to the nearest tenth.
- Round 3.14159 to the nearest hundredth.
- Round 9.95 to the nearest tenth.
- Round $4.876 to the nearest cent.
- Round 0.4449 to the nearest thousandth.
Answers: 1) 7.3 2) 3.14 3) 10.0 4) $4.88 5) 0.445
Quick recap
- Check the digit after the rounding digit: 5 or more rounds up.
- Carry when a 9 rounds up; keep trailing zeros to show precision.
- Round only the final answer.