We performed optical spectroscopy measurement on single crystals of BaFe2As2 and SrFe2As2, the parent compounds of FeAs-based superconductors. Both are found to be quite metallic with fairly large plasma frequencies at high temperature. Upon entering the spin-density-wave state, the formation of partial energy gaps was clearly observed with the surprising presence of two different energy scales. A large part of the Drude component was removed by the gapping of Fermi surfaces. Meanwhile, the carrier scattering rate was even more dramatically reduced. We elaborate that the spin-density-wave instability is more likely to be driven by the Fermi surface nesting of itinerant electrons than a local-exchange mechanism.