The live-fraction check is source-bound to the dead-time budget. 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 live fraction cites the dead-time source

The live-fraction check cites 3 fields from the dead-time budget: clock, live time, and rate.

3 source fields3\ \text{source fields}
Live fractionLive fraction scales the useful rate.live=4 seffective=2/3 HzclockTime=12 sliveTime=4 sliveFraction=1/3 ratioinputRate=2 HzeffectiveRate=2/3 Hz

A same-valued fraction from another budget is not enough

The source contract keeps the 4 second live time tied to this 12 second clock.

Tlive=4,T=12T_{\text{live}}=4,\quad T=12
Live fractionLive fraction scales the useful rate.live=4 seffective=2/3 HzclockTime=12 sliveTime=4 sliveFraction=1/3 ratioinputRate=2 HzeffectiveRate=2/3 Hz