We explicitly demonstrate that current numerical relativity technology is able to accurately evolve black hole binaries with mass ratios of the order of 1000:1. This has direct implications for future third generation (3G) gravitational wave detectors and space mission LISA, as by purely numerical methods we are able to accurately compute gravitational waves, as directly predicted by general relativity. We perform a sequence of simulations in the intermediate to small mass ratio regime, mp1/mp2=1/7,1/16,1/32,1/64,1/128,1/256,1/512,1/1024, with the small hole starting from rest at a proper distance D≈13M. We compare this full numerical evolutions with the corresponding semianalytic perturbative results finding a striking agreement for the total gravitational radiated energy and linear momentum as well as for the gravitational waveforms. We display numerical convergence of the results and identify the minimal numerical resolutions required to accurately solve these very low amplitude gravitational waves. We conclude that we have the numerical technology to build up template banks in time for 3G detectors and LISA.