This paper introduces an accurate position control algorithm based on Backward-Euler discretization of a second-order sliding mode control (SOSMC) and the super-twisting observer (STO). This position control algorithm does not produce numerical chattering, which has been known to be a major drawback of explicit implementation of SOSMC and STO. It is more accurate than the conventional PID control that is also free of chattering. In contrast to conventional Backward-Euler discretization schemes of SOSMC and STO, the presented discretization method does not require any special solvers for computation. The accuracy and implementation of this algorithm are illustrated by simulations.