Number representation can be used for representing the coefficients of the digital filter as a means of reducing the multiplication size and improved the computation speed. However, when each coefficient is rounded to the different number representations, their quantization different error is caused. This quantization round-off error of coefficients can influence the magnitude of the stopband attenuation when implementing the finite impulse response(FIR) low pass filter(LPF). The number representation systems here include two’s complement number representation sys tem, canonical signed digit(CSD) number representation system and sum of power-of-two(SPT) number representation system. In this work, we analyze the round-off error of coefficient of digital filter using different number representation systems and give the probability density distribution of round-off error at various word-lengths. As the SPT number representation is also related to the Hamming weight K, the probability density distribution changes with varies the value of the K. Then implementing the FIR LPF filter with the different number system to find out the influence of coefficients quantization on the stopband attenuation. Furthermore, a cost function is used to connect the computation size and filter performance together to find a FIR LPF which has acceptable performance and quicker computation. This cost function is used to indicate the proper word-length and filter length for approximate FIR LPF which achieved by different number representations systems. After comparison of 1159 of approximate FIR LPF used different number representation, we try to find out the suitable number representation which can make the approximate filter has better filter performance and lowest computation size.