It is often supposed that mathematical argument provides a model of precision for the sciences. In contrast to this view, the present article proposes to distinguish between mathematical exactness as a ideal regulating the inner standards of mathematical argumentation and precision as a norm governing the relation between products of mathematical reasoning in scientific contexts and empirical or practical data. By discussing a major achievement in the mathematization of flight, Ludwig Prandtl's lifting line theory of wings, it is shown that (...) exact reasoning does not necessarily lead to scientific precision, and that the achievement of precision may even require to loosen existing standards of exactness. It is argued that the main contribution of mathematical argument to generating precision in science lies in its capacity to provide sophisticated tools for the production of data, rather than in its adherence to an ideal of exactness. (shrink)