Rounding Calculator
Round to decimal places or significant figures, and see how the different tie-breaking rules change the answer.
Formula
Round half up: 0.5 and above goes up, below 0.5 goes down
- Banker’s rounding sends an exact half to the nearest even number
- Significant figures count from the first non-zero digit
2.5 rounds to 3 half-up, but to 2 under banker’s rounding
Decimal Places Versus Significant Figures
Decimal places count digits after the point. Significant figures count meaningful digits from the first non-zero one.
0.004567 to 2 decimal places is 0.00 — useless. To 2 significant figures it is 0.0046, which preserves the information.
Significant figures are the better choice whenever values span very different magnitudes, which is why science uses them.
Which Way Does 2.5 Go?
Exact halves need a tie-breaking rule, and there is more than one:
- Round half up: 2.5 becomes 3. Taught in schools, and what most people expect.
- Round half to even (banker's rounding): 2.5 becomes 2, while 3.5 becomes 4. Always rounds towards the even neighbour.
Banker's rounding exists because always rounding halves upward introduces a small upward bias, which compounds badly across thousands of financial records. It is the IEEE 754 default, and the reason a spreadsheet occasionally disagrees with your mental arithmetic.
Round Once, at the End
Rounding intermediate results accumulates error. Carry full precision through a calculation and round only the final answer.
Be aware too that binary floating point cannot represent every decimal exactly: 0.1 + 0.2 gives 0.30000000000000004 in most programming languages. That is not a bug but a consequence of base-2 storage, and it is why financial software stores amounts in whole pence rather than fractional pounds.
Quick Reference
| Value | Half up | Half down | Banker’s | 2 decimal places |
|---|---|---|---|---|
| 2.5 | 3 | 2 | 2 | 2.50 |
| 3.5 | 4 | 3 | 4 | 3.50 |
| 2.345 | 2 | 2 | 2 | 2.35 |
| −2.5 | −3 | −2 | −2 | −2.50 |
| 0.125 | 0 | 0 | 0 | 0.13 |
Frequently Asked Questions
- What is the difference between decimal places and significant figures?
- Decimal places count digits after the point; significant figures count meaningful digits from the first non-zero one. For very small numbers, significant figures preserve far more information.
- Does 2.5 round to 2 or 3?
- It depends on the rule. Round half up gives 3; banker's rounding gives 2, because it rounds to the nearest even number to avoid systematic upward bias.
- What is banker's rounding?
- Rounding exact halves to the nearest even digit. It prevents the small upward bias that always rounding up would introduce across large data sets.
- Why does 0.1 + 0.2 not equal 0.3 on a computer?
- Binary floating point cannot represent those decimals exactly, so tiny errors appear. Financial systems avoid it by working in whole pence.