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As application complexity increases, modern embedded systems have adopted heterogeneous processing elements to enhance the computing capability or to reduce the power consumption. The heterogeneity has introduced challenges for energy efficiency in hardware and software implementations. This paper studies how to partition real-time tasks on a platform with heterogeneous processing elements (processors) so that the energy consumption can be minimized. The power consumption models considered in this paper are very general by assuming that the energy consumption with higher workload is larger than that with lower workload, which is true for many systems. We propose an approximation scheme to derive near-optimal solutions for different hardware configurations in energy/power consumption. When the number of processors is a constant, the scheme is a fully polynomial time approximation scheme (FPTAS) to derive a solution with energy consumption very close to the optimal energy consumption in polynomial-time/space complexity. Experimental results reveal that the proposed scheme is very effective in energy efficiency with comparison to the state-of-the-art algorithm.