A refrigeration unit extracts energy from a cold space at $T_c$ and transfers energy as heat to a warm environment at $T_h$. A Carnot refrigerator defines the ideal case, and its coefficient of performance is defined by
$$C.O.P. = \frac{T_c}{T_h - T_c}$$
Assume equal uncertainties (in $^\circ C$) in the measurement of $T_c$ and $T_h$. How well must the temperature measurements be made for this ideal $C.O.P.$ to be determined to within 1% when the nominal value of $T_c$ and $T_h$ are $-10^\circ C$ and $20^\circ C$, respectively?