The book pins squared response so cutoff does not require a decimal amplitude. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The exact cutoff claim is squared response

The raw amplitude at cutoff is not pinned as a decimal; the checked claim is 1/2 of the squared signal budget.

use H2=12, not a rounded amplitude\text{use } |H|^2 = {1\over 2}, \text{ not a rounded amplitude}
Squared responseThe visible ratio is exact.ffcratioinoutlowpass

The mean-square budget halves exactly

Input budget 20 becomes output budget 10.

2012=1020\cdot {1\over 2} = 10
Half budgetThe output bar is bound to the checked budget.ffcratioinoutlowpass