Since the initial demonstration of the ability to experimentally isolate a single graphene sheet, a great deal of theoretical work has focused on explaining graphene's unusual carrier-density-dependent conductivity σ(n), and its minimum value (σmin) of nearly twice the quantum unit of conductance (4e2/h) (refs 1, 2, 3, 4, 5, 6). Potential explanations for such behaviour include short-range disorder, `ripples' in graphene's atomic structure and the presence of charged impurities. Here, we conduct a systematic study of the last of these mechanisms, by monitoring changes in electronic characteristics of initially clean graphene as the density of charged impurities (nimp) is increased by depositing potassium atoms onto its surface in ultrahigh vacuum. At non-zero carrier density, charged-impurity scattering produces the widely observed linear dependence of σ(n). More significantly, we find that σmin occurs not at the carrier density that neutralizes nimp, but rather the carrier density at which the average impurity potential is zero. As nimp increases, σmin initially falls to a minimum value near 4e2/h. This indicates that σmin in the present experimental samples is governed not by the physics of the Dirac point singularity, but rather by carrier-density inhomogeneities induced by the potential of charged impurities.