Unit content
Uncertainty budgets and reporting measurement results
A complete measurement result combines an estimate of the measurand with a transparent account of the important uncertainty sources. An uncertainty budget lists those sources, quantifies their standard uncertainties, and propagates them through the measurement model.
Suppose a speed is calculated from $v=L/t$. The uncertainty budget might include repeated timing scatter, timer calibration, distance calibration, uncertainty in identifying the start and end positions, and environmental effects. Each source is expressed as a standard uncertainty in an input quantity and propagated to $v$ according to its sensitivity.
If the relevant contributions to $v$ are independent and equal to $0.10$, $0.05$, and $0.04,\mathrm{m/s}$, the combined standard uncertainty is $$u_v=\sqrt{0.10^2+0.05^2+0.04^2}\approx0.12,\mathrm{m/s}.$$ A result might therefore be reported as $$v=(12.43\pm0.12),\mathrm{m/s},$$ with text stating that the uncertainty is one combined standard uncertainty and identifying the measurement model.
Sometimes an expanded uncertainty $U=ku$ is reported, where the coverage factor $k$ is chosen to give a wider interval under stated assumptions. The value of $k$ and the interpretation of the interval should be explicit rather than hidden behind a bare $\pm$ symbol.
Significant digits should reflect uncertainty: reporting $12.428731\pm0.12$ suggests precision unsupported by the experiment. Conversely, aggressive rounding can discard useful information.
An uncertainty budget is not bookkeeping for its own sake. It reveals what limits the experiment. If one calibration term dominates all others, collecting ten times more repeated measurements will achieve little; improving the dominant source is the rational next step.