Imprecise computation has been suggested as a promising model of real-time computing in order to deal with timing constraints imposed by the environment. However, the theoretical foundation of the technique has not been fully explored. To address this, a decision-theoretic foundation of imprecise computation is proposed. The main benefit of such a treatment is that it enables the qualitative assumptions underlying imprecise computation techniques to be explicitly stated in a formal way. The theoretical foundation laid out in this paper, hence, will not only enable the justification of using imprecise computation techniques for a real-time application, but will also facilitate the development of extended techniques for more complexs real-time systems.