How to round a number
The steps below describe standard half-up rounding. Other rounding rules, such as banker’s rounding, can give a different result when the number is exactly halfway between two values.
- Find the last digit you want to keep.
- Look at the next digit to its right — the deciding digit.
- If it’s 5 or more, add one to the last kept digit. If it’s less than 5, leave it.
- Drop every digit after the kept ones (or replace them with zeros, if they’re before the decimal point).
Rounding 3.14159 to 2 decimal places: the kept digits are 3.14, the deciding digit is 1, which is less than 5, so the answer is 3.14. Rounding 2.675 to 2 decimal places: the deciding digit is 5, so the 7 becomes an 8 and the answer is 2.68.
Rounding examples
| Number | Rounded to | Result |
|---|---|---|
| 3.14159 | 2 decimal places | 3.14 |
| 2.675 | 2 decimal places | 2.68 |
| 1.005 | 2 decimal places | 1.01 |
| 7.8 | Whole number | 8 |
| 2.5 | Whole number | 3 |
| -2.5 | Whole number | -3 |
| 0.0449 | 2 decimal places | 0.04 |
| 9.999 | 2 decimal places | 10.00 |
| 1234 | Nearest 10 | 1,230 |
| 1250 | Nearest 100 | 1,300 |
| 499 | Nearest 1,000 | 0 |
| 56,789 | Nearest 1,000 | 57,000 |
Decimal place names
- 1 decimal place — tenths: 3.1
- 2 decimal places — hundredths: 3.14
- 3 decimal places — thousandths: 3.142
- 4 decimal places — ten-thousandths: 3.1416
- 5 decimal places — hundred-thousandths: 3.14159
- 6 decimal places — millionths: 3.141593
Rounding to 2 decimal places is the same as rounding to the nearest hundredth, and it’s the precision money uses.
Rounding to the nearest 10, 100 or 1,000
The same rule works to the left of the decimal point. To round to the nearest 100, keep the hundreds digit and look at the tens digit: 1,250 becomes 1,300 because the tens digit is 5. Dropped digits become zeros rather than disappearing, so the number keeps its size. Rounding 499 to the nearest 1,000 gives 0, since it’s nearer 0 than 1,000.
Rounding negative numbers
Standard rounding treats negative numbers as a mirror image of positive ones: −2.5 rounds to −3, just as 2.5 rounds to 3. Halves go away from zero, whatever the sign.
Not all software agrees. JavaScript’s Math.round(-2.5)
returns −2, because JavaScript’s Math.round() uses a different rule for
negative half values. This calculator follows the school rule.
Rounding rules compared
| Number | Standard | Banker’s | Always up | Always down |
|---|---|---|---|---|
| 2.5 | 3 | 2 | 3 | 2 |
| 3.5 | 4 | 4 | 4 | 3 |
| 2.1 | 2 | 2 | 3 | 2 |
| −2.5 | −3 | −2 | −2 | −3 |
| −2.1 | −2 | −2 | −2 | −3 |
- Standard (half up) is what schools teach: halves round away from zero.
- Banker’s rounding (half to even) sends exact halves to
the nearest even digit, so 2.5 becomes 2 but 3.5 becomes 4. It is
designed to reduce systematic rounding bias when many values are
rounded. Python’s
round()uses it:round(2.5)is 2. - Ceiling moves to the next value above whenever anything is dropped — useful when you need "at least", such as how many boxes to buy.
- Floor moves to the next value below — useful when you need "no more than".
"Up" and "down" mean toward positive and negative infinity. For a negative number, rounding up moves toward zero: −2.1 rounds up to −2.
Don’t round in stages
Always round from the original number in a single step. Rounding 0.0449 to 2 decimal places gives 0.04, because the deciding digit is 4. Rounding it to 3 places first gives 0.045, and rounding that to 2 places gives 0.05 — a different, wrong answer, created entirely by the extra step.
Why some apps round 2.675 to 2.67
Computers store most decimals in binary, which can’t represent them
exactly. The number 2.675 is stored slightly below the exact decimal
value, so a rounding operation can produce 2.67 instead of 2.68.
JavaScript’s (2.675).toFixed(2) gives "2.67", and Python’s
round(2.675, 2) gives 2.67. The same kind of floating-point
issue can turn 1.005 into 1.00.
This calculator never converts your number to binary. It works on the digits exactly as you typed them, so under standard half-up rounding, 2.675 rounds to 2.68 and 1.005 rounds to 1.01.
Frequently asked questions
How do you round to 2 decimal places?
Look at the third digit after the decimal point. If it’s 5 or more, add one to the second digit; if it’s less than 5, leave the second digit alone. Then drop everything after the second digit. 3.14159 becomes 3.14, and 2.675 becomes 2.68.
Does 5 round up or down?
In standard rounding, 5 rounds up — away from zero — so 2.5 becomes 3 and −2.5 becomes −3. Banker’s rounding is the exception: it rounds an exact half to the nearest even digit, so 2.5 becomes 2.
What is 1,250 rounded to the nearest hundred?
1,300. The tens digit is 5, so the hundreds digit goes up by one. With banker’s rounding, 1,250 becomes 1,200 because 1,250 is exactly halfway between 1,200 and 1,300, and 1,200 is the even hundred.
Why is my spreadsheet or code rounding differently?
Usually for one of two reasons. Some tools use banker’s rounding by default, as Python’s round() does. Others store decimals in binary, which slightly misrepresents values like 2.675 and tips them the wrong way. This calculator avoids both: it uses the standard rule unless you choose otherwise, and it works on the exact digits you entered.
Should I keep trailing zeros?
Yes, when they show precision. 3.1 rounded to 2 decimal places is written 3.10, which shows the result to the hundredth place. Dropping the zero would suggest less precision than you have.