Conventional hard real-time scheduling is often overly pessimistic due to the worst case execution time estimation. The pessimism can be mitigated by exploiting imprecise computing in applications where occasional small errors are acceptable. This leverage was previously investigated for preemptive scheduling. We study how to make use of imprecise computing in uniprocessor non-preemptive real-time scheduling, which is known to be more difficult than its preemptive counterpart. Several heuristic algorithms are developed for periodic tasks with independent or cumulative errors due to imprecision. Simulation results show that the proposed techniques can significantly improve task schedulability and achieve desired accuracy-schedulability tradeoff. The benefit is further confirmed by a prototyping implementation in Linux system.