Schematic example of a probability distribution of a variable that covers several orders of magnitude and that is fairly uniformly distributed on a logarithmic scale. The sum of the area of the blue bins is the relative probability that the first significant digit equals 1 (d = 1), while the sum of the area of the red bins is the relative probability that the first significant digit equals 8 (d = 8). Because the distribution is fairly uniform, i.e. the bin heights are roughly the same, the cumulative red and blue areas are foremost proportional to the fixed widths of the red and blue bins, respectively, such that numbers randomly drawn from this distribution will approximate Benford’s law.