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…is quoted without an accompanying uncertainty, the number cannot be compared against another laboratory’s figure, however precise the instrument sounds. The combined standard uncertainty $u_c(y)$ for a measured quantity y = f($x_1$, $x_2$, $\ldots$, $x_N$) that is a function of several independently uncertain inputs is, to first order, $u_c^2(y) = \sum_{i=1}^{N} \left( \frac{\partial f}{\partial x_i} \right)^2 u^2(x_i)$. which is the law of propagation of uncertainty the GUM formalizes [ 2 ] . This equation matters here because it is the reason a headline resolution figure for any of…

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