Hartree-Fock Roothaan (HFR) calculations for ground states of the neutral atoms from He to Sr have been performed using integer and noninteger Slater type orbitals (n- and ni-STOs). In addition, we calculated three largest relativistic corrections which are the relativistic kinetic energy correction, the Darwin term and spin-orbit interaction using n-STOs as perturbation. It has been seen that 1s electrons are responsible for almost 80-90% of the total relativistic kinetic energy and the Darwin corrections. Besides, it has been observed that while the total relativistic energy corrections for small atoms change between 0 and –1 au, the magnitude of the corrections increases rapidly when going through the bigger atoms. The results show that the kinetic energy correction and Darwin correction terms may not be neglected in an accurate calculation even for small atoms. Our results are in accord with the other results found in the literature.