Because "3 sig figs" means different things in different classes
Convention Switcher
Pick a course or standard and see how it rounds your number — and exactly what changes from the School Standard. The methods differ on an exact tie: a trailing 5 with nothing after it.
The six conventions split into two answers for 2.5 to 0 decimal places:
| Convention | Tie rule | Answer |
|---|---|---|
| School Standard selected | half up | 3 |
| AP Chemistry | half up | 3 |
| IB Sciences | half up | 3 |
| ASTM E29 | half to even | 2 Δ |
| NIST / GUM | half to even | 2 Δ |
| IEEE 754 | half to even | 2 Δ |
School Standard
Common classroom practiceThe common pre-college and general-chemistry classroom convention.
- Tie rule
- Round half up: a trailing 5 rounds the last kept digit up, away from zero, so 2.5 becomes 3.
- Also distinctive
- Count significant figures with the standard five rules. Keep a guard digit or two through a multi-step calculation and round once at the end.
- Common convention in US general-chemistry and pre-college textbooks.
- Widely taught "five significant-figure rules" and round-half-up tie rule.
AP Chemistry
Common classroom practiceCollege Board AP Chemistry classroom and exam practice.
- Tie rule
- Commonly round half up, as in most US chemistry classes.
- Also distinctive
- AP exam scoring generally penalizes significant-figure errors only once across the free-response section and accepts an answer within one digit in the last significant place, so a half-even result is normally still credited.
AP is a trademark registered by the College Board, which was not involved in producing, and does not endorse, this site.
- College Board, AP Chemistry Course and Exam Description (scoring guidance on significant figures).
- College Board AP Chemistry free-response scoring guidelines (one significant-figure penalty per exam).
IB Sciences
Common classroom practiceInternational Baccalaureate Diploma science subjects.
- Tie rule
- Commonly round half up.
- Also distinctive
- Report measured and calculated values to a number of significant figures consistent with the precision of the instrument or raw data. Quote uncertainties (usually to one significant figure) and match the value's last decimal place to the uncertainty.
IB and International Baccalaureate are trademarks of the International Baccalaureate Organization, which was not involved in producing, and does not endorse, this site.
- IB Diploma Programme science subject guides (data analysis and internal-assessment requirements).
- IB sciences assessment guidance on significant figures and uncertainties.
ASTM E29
Rule set by a standardUsing significant digits in test data to determine conformance with specifications.
- Tie rule
- Round half to even under the standard's rounding method: a trailing 5 leaves an even last digit unchanged and rounds an odd one up, so 2.5 becomes 2 and 3.5 becomes 4.
- Also distinctive
- For conformance testing, round the observed value to the same place as the specification limit before comparing (the rounding method), unless an absolute method is specified instead.
- ASTM E29, Standard Practice for Using Significant Digits in Test Data to Determine Conformance with Specifications (rounding method).
- ASTM International standard summary; the full text is copyrighted and paraphrased here.
NIST / GUM
Rule set by a standardUS metrology guidance and the Guide to the Expression of Uncertainty in Measurement.
- Tie rule
- Round half to even, the rule recommended for reporting rounded values.
- Also distinctive
- Professional metrology reports a value with a combined standard uncertainty rather than relying on significant figures. State the uncertainty to one or two significant figures and round the value to the same last place.
- NIST Special Publication 811, Appendix B (guidance on rounding).
- JCGM 100 (GUM), Evaluation of measurement data: Guide to the expression of uncertainty in measurement, clause 7 (reporting).
IEEE 754
Rule set by a standardThe binary floating-point arithmetic standard used by computers.
- Tie rule
- The default rounding attribute is round to nearest, ties to even (roundTiesToEven).
- Also distinctive
- IEEE 754 governs binary floating point, where a 64-bit double holds about 15 to 17 significant decimal digits and fractions such as 0.1 have no exact binary form. That is why software can disagree with hand calculation, and why this site computes with exact integers instead.
- IEEE Std 754-2019, IEEE Standard for Floating-Point Arithmetic, clause 4.3 (rounding-direction attributes).
- IEEE 754 default rounding attribute roundTiesToEven.
Why the same number gets marked differently
Counting significant figures is nearly universal, but rounding an exact tie is not. A tie is a discarded 5 with only zeros after it, such as 2.5 rounded to a whole number. Round half up gives 3; round half to even gives 2. Both are correct under their own convention, which is why a classroom answer and a conformance-test answer can disagree on the same input.
On any input that is not an exact tie, all six conventions here produce the same rounded value. The switcher makes that explicit so you can tell a genuine convention difference from an arithmetic mistake.
Differences beyond rounding
Conventions also differ in ways this tool does not compute, described on each card: AP Chemistry tolerates an answer within one digit in the last place; IB matches precision to the instrument and quotes uncertainties; NIST and the GUM report a value with a combined standard uncertainty instead of relying on significant figures; and IEEE 754 concerns binary floating point, where fractions like 0.1 are not exact. Follow the specific rule your course or standard states; editions and instructors vary.
Related tools
See all six rounding methods on one input in the Rounding Mode Comparator, round with full working in the Round to N Significant Figures tool, or evaluate expressions in the Significant Figures Calculator.
Method, sources, and limits
The live answer applies each convention's tie-breaking rule to the exact digits of the input using decimal strings on the server and the shared BigInt engine in the browser. The guidance and citations are paraphrased from the sources named on each card; standard text is copyrighted and is not reproduced. This tool summarizes common or documented practice and is not affiliated with, or endorsed by, any exam board or standards body.
Changelog
- Initial release comparing six rounding conventions with a live diff and cited per-convention guidance.