In science, a potential answer to a problem is either right or wrong. But when it comes to teaching and learning, and especially grading student exams, there is wrong and then there is WROOONG.
Here’s an example. Let’s say you need to compute a certain distance that has to do with the behavior of electrons in a nanostructure.
Correct answer: 160 nm
Wrong: 300 nm (wrong, but within the order of magnitude)
More wrong: 1.6 μm or 1.6 nm (wrong order of magnitude, but still meaningful, within the scales of nanostructures)
Nonsensically wrong: 1.6 m (height of an adult woman) or 1.6 fm (size of an atomic nucleus; fm=10^(-15) m). While it may seem that mistaking the 160-nm length for a macroscopic height of a woman is more silly and thus more wrong than the nuclear size, the latter is actually “wronger” because it is 8 orders of magnitude off (versus 7 orders of magnitude for the former).
Two things that we don’t teach our students enough, that we perhaps don’t insist enough on, are minding units and building intuition about orders of magnitude. They are amazing, priceless tools for sanity checking.