Holding force fixed while distance changes shows work as a proportional area, not a single multiplication. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Two metres under six newtons gives twelve joules
Hold force at 6 newtons. A 2 metre pull makes work 12 joules.
6⋅2=12
Four metres doubles the work
The force remains 6 newtons while distance grows to 4 metres, so the checked area is 24 joules.
6⋅4=24
Six metres makes the original audit work reappear
Distance 6 metres under force 6 newtons gives 36 joules, matching the capstone audit work.