We present the concept of approximate intermittent computing and concretely demonstrate its application. Intermittent computations stem from the erratic energy patterns caused by energy harvesting: computations unpredictably terminate whenever energy is insufficient and the application state is lost. Existing solutions maintain equivalence to continuous executions by creating persistent state on non-volatile memory, enabling stateful computations to cross power failures. The performance penalty is massive: system throughput reduces while energy consumption increases. In contrast, approximate intermittent computations trade the accuracy of the results for sparing the entire overhead to maintain equivalence to a continuous execution. This is possible as we use approximation to limit the extent of stateful computations to the single power cycle, enabling the system to completely shift the energy budget for managing persistent state to useful computations towards an immediate approximate result. To this end, we effectively reverse the regular formulation of approximate computing problems. First, we apply approximate intermittent computing to human activity recognition. We design an anytime variation of support vector machines able to improve the accuracy of the classification as energy is available. We build a hw/sw prototype using kinetic energy and show a 7x improvement in system throughput compared to state-of-the-art system support for intermittent computing, while retaining 83% accuracy in a setting where the best attainable accuracy is 88%. Next, we apply approximate intermittent computing in a sharply different scenario, that is, embedded image processing, using loop perforation. Using a different hw/sw prototype we build and diverse energy traces, we show a 5x improvement in system throughput compared to state-of-the-art system support for intermittent computing, while providing an equivalent output in 84% of the cases.