Reporting uncertainty: rounding and significant figures
Report the expanded uncertainty to at most two significant figures, round the result to the same decimal place, and state the coverage factor.
An expanded uncertainty of 0.11734 °C claims knowledge no budget can support. The GUM recommends reporting U to at most two significant figures, and the measured value rounded to the decimal place of U. Rounding of intermediate values is avoided; rounding happens once, at the end.
Examples
- Correction +0.0473 °C, U = 0.0316 °C → report +0.047 °C, U = 0.032 °C (k = 2).
- Reading 21.8367 °C, U = 0.12 °C → report 21.84 °C ± 0.12 °C (k = 2).
Form of words
The GUM suggests a form such as: 'The reported expanded uncertainty is based on a standard uncertainty multiplied by a coverage factor k = 2, providing a level of confidence of approximately 95 %.' Accredited certificates carry an equivalent statement.
Frequently asked questions
- Should U be rounded up or to nearest?
- Round to nearest unless doing so reduces U by more than a few percent, in which case rounding up is the conservative convention.
References
- [1]JCGM 100:2008 — Guide to the expression of uncertainty in measurement (GUM)
- [2]ISO/IEC 17025:2017 — General requirements for the competence of testing and calibration laboratories
General technical guidance written against the cited sources. It is not regulatory or legal advice and does not replace the applicable standard, guideline or a qualified reviewer's judgement.
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Combine Type A and Type B components per the GUM: divisors by distribution, sensitivity coefficients, u_c, effective degrees of freedom and U at k = 2.
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