Recently there has been a renewed interest on the relationship between efficient conic representations of a polytope and (exact) cone factorizations of its slack matrix. Since in practice, one only obtains numerical approximations of cone factorizations, the question of what do these approximations imply in terms of representing the polytope gains importance. In this talk we will present inner and outer convex approximations of a polytope obtained from approximate cone factorizations of a slack matrix of the polytope, and show that if the quality of the approximated factorization is good, so is the approximated lift.