TL;DR
Eight engineering disasters. Zero arithmetic errors. Every single one was caused by two numbers — both correct, both carefully computed — meaning different things on opposite sides of a software interface. One cost $65 billion. Another killed 28 soldiers because 0.1 can't be represented in binary. The fix is never the math. The fix is the label.
There is a particular kind of silence in a control room when someone realizes the number on the screen is in the wrong unit. It lasts about two seconds. Then it's replaced by the kind of noise nobody wants to hear.
On September 23, 1999, that silence happened at the Jet Propulsion Laboratory in Pasadena, California. The Mars Climate Orbiter had just disappeared behind the planet. Telemetry showed the spacecraft at 57 kilometers above the surface. It was supposed to be at 140.
The silence was four seconds long. Then someone said "oh no" — the official NASA transcript uses a stronger word — and $327 million of aluminum, titanium, and human effort disintegrated into the Martian atmosphere.
