In chaotic systems, small errors are magnified, bringing into question almost any computer simulation of the system. Shadowing techniques show that under some circumstances the simulated trajectory may be a close approximation to a true trajectory. In the absence of shadowing, long correct trajectories may not be computationally available, and there are open questions about how accurately long-term averages on the underlying space can be computed. We discuss some of

these questions. In particular we propose a scaling law for the bias between the correct time average and the expected value of the computer-simulated time average, as a function of one-step error.