A long while back I wrote about analog math — math with slide rules. One of the features (or perhaps lack thereof depending on your perspective) is the lack of a decimal point.
Without a decimal point you’re forced to keep track of the magnitude of your calculations. You can start to develop a gut feel for how big or small something aught to be. If you wind up with something that’s woefully different then you expect you can take that opportunity to take a step back and revisit your assumptions.
In the case today I didn’t have to have to go to the number of decimal places as most normal applications of Fermi’s technique — but at the same time I was able to reach the conclusion that 0.29% (of some quantity we were looking at at work) seemed mostly outside the realm of possibility.
While I don’t yet know the answer, I can be pretty suspicious of that number. Similarly, acting on that number may well be a fool’s errand as well. If you don’t know what the number really represents it’ll be the source of layered assumptions that may or (likely) may not be correct.