A figure skater is spinning on frictionless ice with their arms outstretched, having an initial rotational inertia \(I_0\) and rotating with angular speed \(\omega_0\). By pulling their arms inward toward their body, the skater reduces their rotational inertia to \(\dfrac{1}{3}I_0\). What is the ratio of the skater's final rotational kinetic energy to their initial rotational kinetic energy, \(\dfrac{K_f}{K_i}\)?