Malus's law says the intensity after a polarizer is I = I0 * cos^2(theta), where theta is the angle between the input polarization and the polarizer axis. The squaring reflects intensity being proportional to amplitude squared. The exact value holds only for a perfectly polarized input and an ideal lossless polarizer; real beams are partially polarized and polarizers leak and absorb, with detector noise and angle error on top.
A polarizer transmits intensity as the squared projection factor. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Malus law squares the projection factor
For one polarizer, transmitted intensity is the source intensity times the squared projection factor.