The passive filter ratio changes the budget before active gain is applied. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
A one-third passive ratio leaves forty after gain
Input budget 30 times passive ratio 1/3 gives passive output 10, then gain 2 gives final 40.
30⋅31⋅22=40
A one-half passive ratio leaves sixty after gain
With the same input and gain, passive ratio 1/2 gives final budget 60.
30⋅21⋅22=60
A two-thirds passive ratio leaves eighty after gain
Passive ratio 2/3 raises the passive output to 20 and final budget to 80.