Extended renormalizations group analysis for quantum gravity and Newton's gravitational constant

The conventional renormalization groups as applied in SU(5) GUT are adapted to the transfinite simplictic arithmetic of E-infinity theory. The resulting simple formalism yielded the exact quantum gravity inverse coupling for non-super symmetric and super symmetric unifications alike. Subsequently by means of analogy supported by Witten's T-duality and black hole theory an accurate estimation of Newton's constant of gravity is derived from what is basically the same formalism.