We propose a different combined approach, which consists of the exact diagonalization, renormalization group, and Bethe ansatz methods, for precise estimates of the charge gap Delta in the one-dimensional extended Hubbard model, with on-site and nearest-neighbor interactions U and V at quarter filling. This approach enables us to obtain the absolute value of Delta, including the prefactor, without ambiguity even in the critical regime of the metal-insulator transition (MIT) where Delta is exponentially small, beyond usual renormalization group methods and/or finite-size scaling approaches. The detailed results of Delta, down to the order of 10(-10) near the MIT, are shown as contour lines on the U-V plane.