https://admiralcloudberg.medium.com/a-mathematical-miracle-t...
This story is more ambiguous. The plane should never have left the ground and the captain committed a serious error when he decided to depart with no fuel gauge working. According to airline procedures at the time, no plane could be dispatched without working fuel gauges. That wasn't up for debate, it was a hard rule and it was disregarded.
Then, contrary to legend, nobody really mixed up imperial and metric units, but they did the math wrong (twice!) when converting from one to the other. They weren't surprised when they found that 8,000 liters of fuel would weight 14,000 kg. One liter of water weights 1 kg; fuel is less dense than water; without knowing anything else, one should question a calculation that results in the weight of 8,000 liters of fuel being more than 8 metric tons.
So yes, ultimately, the plane landed safely thanks to outstanding airmanship; but it was improper following of guidelines, and math incompetence, that caused the problem in the first place.
Also known as the Swiss cheese model[1].