The motional mode is a finite packet ledger. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Motion is counted by packets on a finite ladder
The mode spacing is 2 joules per packet.
Epacket=2J
Packet index two carries four joules of motion
At packet index 2, the motional energy is 4 joules.