 Photometric magnitude uncertainty

For a fixed magnitude zero point, the derivative of $m=-2.5{\log }_{10}(f/f_0)$ gives the small-error propagation of uncertainty formula ${\sigma }_m=(2.5/\ln 10){\sigma }_f/f$. A fractional observed radiative flux uncertainty of $0.1$ gives about $0.109$ mag of absolute uncertainty. A fractional magnitude uncertainty additionally needs the value of $m$, is undefined at $m=0$, and depends on the adopted magnitude zero point.