= Solution
For a fixed <magnitude zero point>, <photometric magnitude uncertainty> follows from <propagation of uncertainty>
$$
\frac{dm}{df}=-\frac{2.5}{f\ln10},\qquad
\sigma_m=\frac{2.5}{\ln10}\frac{\sigma_f}{f}
=\boxed{0.1086\ \mathrm{mag}}.
$$
This is the absolute <standard uncertainty> of the <apparent magnitude>. The requested fractional uncertainty is instead
$$
\boxed{\frac{\sigma_m}{|m|}=\frac{0.1086}{|m|}
=\frac{0.1}{|\ln(f/f_0)|}}.
$$
This is the requested fractional <standard uncertainty> as a function of $m$; \b[there is no single numerical fractional error independent of the magnitude]. At $m=0$ it is undefined. Moreover, its value changes when the <magnitude zero point> changes; the absolute magnitude uncertainty is the useful invariant of such a zero-point shift. Treating the stated percentage as a finite perturbation rather than a <standard uncertainty> gives changes $-0.1035$ mag for $f\mapsto1.1f$ and $+0.1144$ mag for $f\mapsto0.9f$, consistent with the linear estimate.
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