For this very reason, it is commonly used to express the contribution that the Ricci curvature (or rather, the Schouten tensor) and the Weyl tensor each makes to the curvature of a Riemannian manifold.
To illustrate the contributions of the Ricci curvature (or the Schouten tensor) and the Weyl tensor to the overall curvature of a Riemannian manifold, this is frequently employed.