A non-volatile memory (NVM) employing MTJ has a lot of strong points such as read/write performance, best endurance and operating-voltage compatibility with standard CMOS. However, it consumes a lot of energy when writing the data. This becomes an obstacle when applying to battery-operated mobile devices. To solve this problem, we propose an approach to augment the capability of the precision scaling technique for the write operation in NVM. Precision scaling is an approximate computing technique to reduce the bit width of data (i.e. precision) for energy reduction. When writing image data to NVM with the precision scaling, the write energy and the image quality are changed according to the write time and the target bit range. We propose an energy-efficient approximate storing scheme for non-volatile flip-flops and a magnetic random-access memory (MRAM) that allows us to write the data by optimizing the bit positions to split the data and the write time for each bit range. By using the statistical model, we obtained optimal values for the write time and the targeted bit range under the trade-off between the write energy reduction and image quality degradation. Simulation results have demonstrated that by using these optimal values the write energy can be reduced up to 50% while maintaining the acceptable image quality. We also investigated the relationship between the input images and the output image quality when using this approach in detail. In addition, we evaluated the energy benefits when applying our approach to nine types of image processing including linear filters and edge detectors. Results showed that the write energy is reduced by further 12.5% at the maximum.