In Diophantine approximation, it is a classical problem to determine the size of the sets related to ψ approximable set for a given non-increasing function ψ. Jarn`ık showed that the Exact ψ approximable set, i.e., the set of vectors that are ψ approximable but not any better even up to a constant, is non-empty. Bugeaud determined the Hausdorff dimension of the exact set in reals using continued fractions. We extend this result to higher dimensions by translating this problem to studying dynamics on the space of unimodular lattices using Dani’s correspondence. This is joint work with Nicolas de Saxc ́e.