This squared-ratio-avoids-decimal-amplitude lesson keeps the cutoff claim in power-like squared-response form, so the ledger uses 1/2 instead of a rounded amplitude decimal. The 20-to-10 budget row is exact only for the stated ideal squared-ratio model. Real measurements depend on detector bandwidth, source level, component tolerances, loading, calibration, finite precision, and uncertainty.
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.