• A prescribed tracking accuracy containment control scheme for non-affine nonlinear uncertain multi-agent systems is proposed in this paper. In the existing results, the presented strategy just ensure that the containment errors gather to a small neighborhood around the origin. In this note, each containment error can converge to a assigned precision value by the proposed method, and the magnitude of each error can be confirmed precisely before the containment controller is designed. • Two important auxiliary functions are used to help deal with the precision tracking issue. With the aid of these two n-order differentiable functions, the Lyapunov functions can be created. And in combination with adaptive and the backstepping techniques, the technical difficulties of the desire controller design are overcome for non-affine nonlinear uncertain multi-agent systems. • A novel analysis method of containment errors is proposed in this note. By using this method, we can conclude that the convergence error for each agent is a given constant. This paper concentrates on a containment control issue for multi-agent systems in non-affine form with a given accuracy. In comparison with the existing studies on multi-agent systems, precision-based containment control idea is first formulated. With the aid of the proposed strategy, the main merit of this note is that the synchronization errors converge to arbitrary given positive number. Simultaneously, the particular Layapunov functions are constructed by feat of two auxiliary functions. By employing the backstepping and adaptive control technique, the key variables and the actual controller are designed. Unlike the traditional stability analysis, a novel method is used to analyse the convergence of containment errors. In the end, some simulation results demonstrate the correctness for the proposed protocol. [ABSTRACT FROM AUTHOR]