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Continuum and compartmental models are presented as alternative descriptions of the electrical behaviour of a dendrite. The one-dimensional continuum model provides a reference against which the accuracy of compartmental models may be assessed. Traditional compartmental models are shown to be first- and not second-order accurate in the presence of synaptic input contrary to what is often claimed. This reduced accuracy arises from the inability of a traditional model to accurately locate synaptic input. A compartment defined by two potentials is introduced to describe a dendritic section, and the influence of synaptic input to the section is divided between its boundaries by means of a partitioning rule. The new compartmental model, with the same level of discretisation as a traditional model, is an order of magnitude more accurate and precise than traditional compartmental models in the presence of synaptic input. Consequently, the new model provides a more powerful tool for distinguishing between different models of an experiment than is possible using a traditional compartmental model.