Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2014 / Paper 1 / A4 / Solution

Converting all lengths to metres gives $d=3.7276\times 10^{-5}\mathrm{m}$. Logarithmic differentiation givesIf the quoted uncertainties are independent standard uncertainties, monomial uncertainty propagation givesIf the quoted uncertainties instead mean bounds, the first-order conservative fractional error is $0.111$, giving approximately $37.3\pm 4.1\mu \mathrm{m}$. The question does not specify their statistical meaning; these two error conventions should not be combined.