I once encountered a math educator whose personal pet peeve was the "give 110%" meme. He drilled into his students that 100% was the literal maximum. Percent came from "per cent" and 100 per 100 is literally all of them. You can't eat 110% of the nachos. You can't use 110% of the gas tank. You can't raise prices 110%.
If you're like me, that last one probably caught your attention. I asked, if the price of a hot dog goes from \$1 to \$2.10, isn't that a 110% increase. His answer was that a 100% increase in price meant all the possible price increase. In other words, to raise the price of a \$1 hot dog by 100%, the new price must be the value of the rest of everything else in existence. I asked whether that meant that a \$1.50 hot dog was no longer a 50% increase in price, and he said percentages weren't useful for terms like prices and that the appropriate answer was that the price of the hot dog had increased by a factor of 1.5. Students needed to learn that a factor of 1.5 increase did not always equate to a 50% increase.
I'm not always good on my feet and was worried that I was starting to antagonize the man, so I dropped the issue. What would have been the proper way to correct this misconception? Or am I the one who is being dense?