Exact rounding is provided for elementary floating-point arithmetic operations (e.g. in the IEEE standard). Many authors have felt that it should be provided for other operations, in particular for geometric constructions. We show how one may round modular representation of numbers to the closest f.p. representable number, and demonstrate how it can be applied to a variety of geometric constructions. Our methods use only single precision; they produce compact, efficient, and highly parallelizable code. We suggest that they can be applied in other settings when exact computations interact closely with rounded representations.