The classical theory of signal processing assumes that the designed IIR filters are continuous and have infinitely accurate coefficients. However, when developing filters for real-world digital signal processing tasks, it is necessary to take into account the finite precision of the coefficients representation, especially considering the fixed-point arithmetic. In this paper, we propose a new approach, which we call the interval size approach, making it easy to evaluate the actual digital filter response for various fixed-point arithmetic parameters. We provide Illustrative examples to demonstrate the frequency response bounds evolution as an order, cutoff frequency, and signal frequency are varying. We show that the interval size can be used as a well-suited accuracy factor of a digital filter.