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How to Round Numbers
Rounding replaces a number with a nearby value that has fewer digits. The basic rule: look at the first digit being dropped. If it is 5 or greater, increase the last kept digit by one. If it is less than 5, leave the last kept digit unchanged. For example, rounding 3.456 to two decimal places gives 3.46 because the dropped digit (6) is 5 or greater.
Step-by-step process
To round a number to N decimal places, follow these steps.
- Identify the digit in the Nth decimal place. This is the last digit you will keep.
- Look at the digit immediately to its right (position N + 1). This is the deciding digit.
- If the deciding digit is 0, 1, 2, 3, or 4, leave the kept digit unchanged.
- If the deciding digit is 5, 6, 7, 8, or 9, increase the kept digit by one.
- Drop all digits after position N.
When the kept digit is 9 and it needs to increase, it becomes 0 and the increase carries leftward, the same way addition carries. Rounding 2.97 to one decimal place: the deciding digit is 7, so you increase 9 to 10. The result is 3.0.
Worked examples
Each example below applies the same five-step process to a different precision level.
Rounding to the nearest whole number
Round 47.82 to the nearest whole number. The last kept digit is 7 (in the ones place). The deciding digit is 8. Since 8 is 5 or greater, increase 7 to 8. The result is 48.
Round 47.34 to the nearest whole number. The deciding digit is 3. Since 3 is less than 5, keep 7 unchanged. The result is 47.
Rounding to one decimal place
Round 6.849 to one decimal place. The last kept digit is 8 (in the tenths place). The deciding digit is 4. Since 4 is less than 5, keep 8 unchanged. The result is 6.8.
Round 6.851 to one decimal place. The deciding digit is 5. Since 5 meets the threshold, increase 8 to 9. The result is 6.9.
Rounding to two decimal places
Round 12.3467 to two decimal places. The last kept digit is 4 (in the hundredths place). The deciding digit is 6. Since 6 is 5 or greater, increase 4 to 5. The result is 12.35.
The rounding calculator handles all of these cases automatically if you want to verify your work.
Rounding negative numbers
Negative numbers introduce a subtlety. Consider rounding -2.5 to the nearest whole number. The answer depends on which direction “up” means.
With the standard “half up” rule, you round toward the larger magnitude. The digit being dropped is 5, so you increase the last kept digit. That takes -2.5 to -3, because -3 is farther from zero.
Some systems instead define “rounding up” as moving toward positive infinity. Under that convention, -2.5 rounds to -2, because -2 is greater than -2.5 on the number line.
These two approaches give the same result for positive numbers but diverge for negatives. If you are writing software or working with financial data, be aware of which convention your tool uses. JavaScript’s Math.round(-2.5) returns -2, while Python’s built-in round(-2.5) returns -2 as well (Python uses banker’s rounding, explained below).
Five rounding methods
The half-up method described above is the version taught in most classrooms, but it is one of several rounding strategies. Each handles the midpoint (when the deciding digit is exactly 5) differently.
| Method | Rule | Example: round 2.5 | Example: round 3.5 |
|---|---|---|---|
| Half up | When the deciding digit is 5, round away from zero | 3 | 4 |
| Floor | Always round toward negative infinity | 2 | 3 |
| Ceiling | Always round toward positive infinity | 3 | 4 |
| Truncation | Drop the extra digits without adjusting | 2 | 3 |
| Banker’s rounding | When the deciding digit is exactly 5, round to the nearest even number | 2 | 4 |
Floor and ceiling ignore the deciding digit entirely. Floor always moves down (toward negative infinity), and ceiling always moves up (toward positive infinity). Truncation simply removes digits to the right of the desired precision, which is equivalent to rounding toward zero.
The half-up, floor, ceiling, and truncation methods all introduce a systematic bias when applied to large data sets. Half up rounds 5s upward every time, creating an upward skew. Floor and truncation pull values downward. Only banker’s rounding is designed to cancel this bias.
When to use banker’s rounding
Banker’s rounding (also called round-half-to-even) applies a special rule only when the deciding digit is exactly 5 with no nonzero digits after it. In that case, it rounds to the nearest even number rather than always rounding up.
Round 2.5: the nearest even whole number is 2, so the result is 2. Round 3.5: the nearest even whole number is 4, so the result is 4. This means that across many rounding operations, roughly half the midpoint cases round up and half round down, keeping the overall average unbiased.
The IEEE 754 standard for floating-point arithmetic specifies banker’s rounding as the default mode. Most financial systems, statistical software packages, and databases use it for the same reason: summing thousands of rounded values should not drift upward or downward from the true total. Python’s built-in round() function uses banker’s rounding, as do .NET, SQL Server, and many accounting platforms.
If you are rounding a single number for a homework problem, half up is fine. If you are rounding values in a spreadsheet column and the total matters, banker’s rounding preserves accuracy better.
Common mistakes
Rounding twice in sequence. Rounding 2.449 to one decimal place should give 2.4, because the deciding digit is 4. A common error is to first round to two places (getting 2.45), then round that result to one place (getting 2.5). This double rounding produces the wrong answer. Always round once from the original number to your target precision.
Confusing precision and accuracy. Reporting a result as 14.3826 does not make it more accurate than 14.4. If the input values only have two significant figures, the extra decimal places are meaningless noise. Match your rounding precision to the precision of your inputs.
Forgetting the carry. When rounding 9.96 to one decimal place, the deciding digit is 6, so the 9 in the tenths place becomes 10. That carries into the ones place, giving 10.0, not 9.10. The carry propagation follows the same rules as addition.
Treating rounding and truncation as the same thing. Truncating 7.89 to one decimal place gives 7.8. Rounding 7.89 to one decimal place gives 7.9. The distinction matters whenever the deciding digit is 5 or greater. Programming languages have separate functions for these operations (Math.round vs Math.trunc in JavaScript, for example).
For a quick way to verify any rounding result, try the rounding calculator. If you need to count meaningful digits in a measurement, the significant figures calculator applies sig-fig rules directly. And for converting rounded results into percentages, the percentage calculator handles the arithmetic.