Rounding makes results easier to read, but it also removes information. Problems arise when the rounded display is treated as the original measurement or when a value is rounded several times on its way into a table. A useful summary preserves the source value and makes its display convention clear.
State which rounding rule you are using
NIST's conversion guide describes a round-to-nearest convention that sends an exact halfway case to an even final digit. That is a stated convention, not permission to assume every laboratory or software package uses it.NIST SP 811 — Conversion and rounding (opens in a new tab)
| Exact input for this example | Rounded value | Reason |
|---|---|---|
| 7.243 | 7.24 | Below the halfway point |
| 7.247 | 7.25 | Above the halfway point |
| 7.245 exactly | 7.24 | Halfway; final retained digit is even |
| 7.255 exactly | 7.26 | Halfway; final retained digit is even |
The word exactly matters in the last two rows. A displayed 7.245 may itself be rounded from a more detailed value. If you do not have the original precision, do not pretend that the displayed number proves an exact tie.
Avoid rounding an already rounded intermediate
Take the exact illustrative input 7.2451. Rounded directly to two decimal places, it becomes 7.25. If first rounded to three decimal places it becomes 7.245; applying the tie-to-even convention to that intermediate gives 7.24. The two-step route has changed the final answer.
This is a simple reason to keep adequate working precision through a calculation and round at the intended reporting stage. A neat-looking intermediate column can otherwise introduce an error into every later formula that uses it.
A rounded display can conceal a position relative to a limit
Suppose an illustrative minimum is 99.5% and the underlying result is 99.46%. Displayed to one decimal place, the result becomes 99.5%. Numerically, the unrounded value is below the minimum, while the displayed value equals it. Which value the decision process uses must come from the applicable rule.
Do not use this example to overrule a laboratory's documented decision. Its purpose is to show why a reader cannot reconstruct the decision from the rounded display alone. Ask whether comparison occurs before or after specified rounding, and how measurement uncertainty is treated where relevant.
When summarising a certificate, retain its reported decision and value accurately. If you create a rounded display for readability, label it as your presentation and keep the original result accessible. Avoid silently changing a pass/fail conclusion during editorial formatting.
Choose precision appropriate to a converted value
NIST also explains that converted results should retain information consistent with the original value's rounding limits. A unit change can produce a long decimal expansion without adding measurement information.NIST SP 811 — Conversion and rounding (opens in a new tab)
For a report table, preserve the original unit and value in one field and place your conversion in another. Then select the final displayed precision deliberately. This makes it possible to inspect the conversion without mistaking every calculator digit for a supported observation.
If only a rounded source value exists, you cannot recover the discarded digits by converting units or adding zeroes. Report the limitation as part of the record. A plausible extra digit is still invented information.
A practical rounding check
- Retain the original numerical value and unit.
- Identify the rounding convention and target precision.
- Avoid rounding intermediate values unnecessarily.
- Check an exact-halfway example when validating a calculation tool.
- Preserve inequalities and the original conformity decision.
Sources and further detail
- NIST SP 811 — Conversion and rounding (opens in a new tab)
Sections B.7.1 and B.7.2. NIST's stated rounding convention is identified explicitly; no source example is copied.
Sources checked 19 September 2026. Worked examples are illustrative unless a supplied report is explicitly identified. This article has not undergone independent scientific peer review.