Distance spreading and half-layers reduce checked count rates. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Doubling distance quarters the rate
Rate 80 per second at distance 2 metres becomes 20 per second at distance 4 metres.
80÷4=20
Three half-layers divide by eight
3 half-value layers turn 64 per second into 8 per second.
64→32→16→8
A second distance doubling also quarters
Rate 100 per second at distance 3 metres becomes 25 per second at distance 6 metres.