Answer:
[tex]\large \boxed{3.1 \times 10^{11} \, \mu\text{ m}^{2}}[/tex]
Explanation:
1. Convert square decimetres to square metres
[tex]\text{Area} = \text{31 dm}^{2} \times \left (\dfrac{\text{1 m}}{\text{10 dm}}\right )^{2} = \text{0.31 m}^{2}[/tex]
2. Convert square metres to square micrometres
[tex]\text{Area} = \text{0.31 m}^{2} \times \left (\dfrac{\text{1 $\mu$m}}{10^{-6} \text{ m}}\right)^{2} = 3.1 \times 10^{11} \, \mu\text{m}^{2}\\\text{The surface area of the desk is $\large \boxed{\mathbf{3.1 \times 10^{11} \, \mu} \textbf{ m}^{2}}$}[/tex]