The brain learns an internal model of the world by making predictions about upcoming inputs and comparing its predictions with actual incoming sensory information. Prediction errors are essential for learning an accurate internal representation of the world because they indicate where the internal representation needs to be improved to make a better prediction in the future. Promisingly, a neural correlate for prediction errors has been found in the activity of pyramidal neurons in layer 2/3 of diverse cortical areas. To make contextually appropriate predictions in a stochastic environment, the brain needs to take uncertainty into account. How uncertainty modulates prediction errors and hence learning is, however, unclear. Here, we use a normative approach to derive how prediction errors should be modulated by uncertainty and postulate that such uncertainty-weighted prediction errors (UPE) are represented by layer 2/3 pyramidal neurons. We then implement the calculation of the UPEs in a biologically plausible microcircuit model of layer 2/3. In particular, in our theory, the UPE reflects the optimal update of the prediction that maximises the likelihood of the incoming sensory inputs given the prediction. The optimal update is the difference between the predicted mean and the sensory input scaled inversely by the uncertainty. Interestingly, pyramidal cells are modulated by both subtractive and divisive inhibition from somatostatin (SST) and parvalbumin (PV) interneurons, respectively. We, therefore, hypothesise that the layer 2/3 circuit calculates the UPE through the subtractive inhibition by SSTs and the divisive inhibition by PVs. We show that (1) PVs can learn to represent the uncertainty in both positive and negative prediction error circuits with a biologically plausible plasticity rule, (2) the inhibitory connections from SSTs to PVs are essential for estimating the uncertainty, and (3) the resulting UPE can be used to update the internal representation of the predicted mean.