My last post turned out to have some bogus calculations - adding/dropping zeroes, a rich source of careless error - which by one of those semi-happy accidents turned out to yield a correct final result - unless you looked at it too closely. H/T to commenter nqdp for wondering out loud why my figures didn't all quite make sense.
I've corrected the errors (or so I hope), while preserving the original text for posterity.
The stakes in this case were remarkably low; at worst I wasted a few hours of your collective time. In real world applications, of course, the cost of brain dead errors is higher, and the errors will hardly ever be neatly offsetting. The example that comes first to mind is the infamous feet/meters fail that did it for the Mars Climate Orbiter. There are of course many others.
Murphy is an Old Testament style prophet, not a gentle father confessor. He comes into your lab or shop to thunder a warning, not give absolution after an error has blown up in your face.
The image of the Gulf of Mexico is from NASA.