The authors have investigated the multifractal scaling of conductance jumps in a hierarchical percolation lattice, resulting from cutting the current carrying bonds in the lattice. Due to the iterative nature of the model, exact renormalization group (RG) equations are obtained and used to extract the minimum conductance jump of the lattice. They find an asymptotically analytic expression for the minimum conductance jump, Delta g_min approximately=exp(-c(log L)²) decreasing faster than any power law. They observed slow convergence to the asymptotic behaviour due to the importance of the irrelevant terms in the RG equations at low generations of the lattice. Numerical calculations are performed in order to validate the analytic results and to calculate the f- alpha spectrum to confirm left-sided multifractality as proposed by Lee and Stanley (1988).