The application of approximate computing (AC) in optimizing tradeoffs among performance, power consumption, and accuracy of computation results can be improved by adjusting data precision in applications. The importance of AC has increased over the years as it is used to maximize performance even with limited power budget and hardware resources in high performance computing (HPC) systems that require more precise computations. To apply AC for HPC applications effectively, we must consider the character of each message passing interface (MPI) rank in an application and optimize it by adjusting its data precision. This rank-level AC ensures that ranks and threads in an application run with data precision and perform data transfer while converting the precision of target data. In this paper, we have proposed and evaluated data pack/unpack application programming interfaces (APIs), which are applicable for standard MPI programs run on HPC systems, for converting the precision of target data. The proposed APIs enable us to express data transfer among ranks with different precisions. In addition, we have also developed a reasonable performance model to select an appropriate data transfer API for maximizing performance with rank-level AC based on performance evaluation with various HPC systems.