Resistive random access memory (ReRAM) is a promising technology that can perform low-cost and in-situ matrix-vector multiplication (MVM) in analog domain. Scientific computing requires high-precision floating-point (FP) processing. However, performing floating-point computation in ReRAM is challenging because of high hardware cost and execution time due to the large FP value range. In this work we present ReFloat, a data format and an accelerator architecture, for low-cost and high-performance floating-point processing in ReRAM for iterative linear solvers. ReFloat matches the ReRAM crossbar hardware and represents a block of FP values with reduced bits and an optimized exponent base for a high range of dynamic representation. Thus, ReFloat achieves less ReRAM crossbar consumption and fewer processing cycles and overcomes the noncovergence issue in a prior work. The evaluation on the SuiteSparse matrices shows ReFloat achieves 5.02x to 84.28x improvement in terms of solver time compared to a state-of-the-art ReRAM based accelerator.