Often, the edge weights of graphs are given in implicitly infinite or overly high precision (think of Euclidean lengths) which leads to both theoretical as well as practical challenges. In this paper we investigate how to round edge weights of a given graph G(V,E,w) such that the rounded weights of paths satisfy certain consistency criteria. Natural consistency criteria are, for example, preserving optimality of paths, and bounding relative change in weight after the rounding procedure. Low precision edge weights allow for more space efficient implementations, faster arithmetic operations, and in general more stable and efficient algorithms. We present an ILP based rounding approach as well as a greedy rounding heuristic. We show experimentally for large road networks and grid graphs that our new rounding approaches are significantly better than common deterministic or randomized rounding schemes.