Systems based on exact arithmetic are very slow. In practical situations, very few computations need be performed exactly as approximating the results is very often sufficient. Unfortunately, it is impossible to know at the time when the computation is called for whether an exact evaluation will be necessary or not. The arithmetic library presented here achieves laziness by postponing any exact computation until it is proved to be indispensable. This yields very substantial gains in performance while allowing exact decisions. The lazy arithmetic techniques are presented in the context of rational computations, using the field of computational geometry as a background.>