What is 1/288 in base 12? A walk through the problem is greatly appreciated

\(288_{10} = 2\cdot 144 = 2\cdot 12^2 \Rightarrow 200_{12}\\ {\dfrac{1}{288}}_{10} = {\dfrac{1}{200}}_{12}\\ \text{Did you want the duodecimal representation?}\\ \dfrac{\frac{1}{288}}{\frac{1}{12^3}} = 6\\ \dfrac{1}{288}_{10} = 0.006_{12} \)

Thank You!