The useful count rate is the incident rate scaled by the live fraction, so dead time reduces the rate ledger before comparison. The scaling is exact only for the stated rate and fraction; real rate corrections depend on detector recovery, pileup, rate dependence, threshold settings, and statistical uncertainty.
Effective rate is the incident rate times live fraction. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Live fraction scales the usable rate
An input rate of 2 hertz with live fraction 1/3 gives an effective rate.