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Energy efficiency is one of the most critical issues in the design of wireless sensor networks. Observing that many sensor applications for object tracking can tolerate a certain degree of imprecision in the location data of tracked objects, this paper studies precision-constrained approximate queries that trade answer precision for energy efficiency. We develop an energy-conserving approximate storage (EASE) scheme to efficiently answer approximate location queries by keeping error-bounded imprecise location data at some designated storage node. The data impreciseness is captured by a system parameter called the approximation radius. We derive the optimal setting of the approximation radius for our storage scheme based on the mobility pattern and devise an adaptive algorithm to adjust the setting when the mobility pattern is not available a priori or is dynamically changing. Simulation experiments are conducted to validate our theoretical analysis of the optimal approximation setting. The simulation results show that the proposed EASE scheme reduces the network traffic from a conventional approach by up to 96 percent and, in most cases, prolongs the network lifetime by a factor of 2-5.