Answer
0.11 degrees C
Work Step by Step
The change in the length is to be less than 1.0 micrometers.
$$\Delta \mathcal{l}=\alpha \mathcal{l}_o \Delta T \lt1.0\times 10^{-6}m$$
$$\Delta T \leq \frac{1.0\times 10^{-6}m }{(9\times 10^{-6}/C^{\circ})(1.0m)}
= 0.11 C^{\circ}$$