Mobile computing is one of the largest untapped reservoirs in today's pervasive computing world as it has the potential to enable a variety of in-situ, real-time applications. Yet, this computing paradigm suffers when the available resources - such as device battery, CPU cycles, memory, I/O data rate - are limited. In this paper, the new paradigm of approximate computing is proposed to harness such potential and to enable real-time computation-intensive mobile applications in resource-limited and uncertain environments. A reduction in time and energy consumed by an application is obtained via approximate computing by decreasing the amount of computation needed by different tasks in an application; such improvement, however, comes with the potential loss in accuracy. Hence, a Mobile Distributed Computing framework, MobiDiC, is introduced to determine offline the 'approximable' tasks in an application and a light-weight algorithm is devised to select the approximate version of the tasks in an application during run-time. The effectiveness of the proposed approach is validated through extensive simulation and testbed experiments by comparing approximate versus exact-computation performance.