An order on magnitude is a factor if 10. So half an order of magnitude is a factor of a square root of ten, or 3.16, because two half orders of magnitude are a

An order on magnitude is a factor if 10. So half an order of magnitude is a factor of a square root of ten, or 3.16, because two half orders of magnitude are a full order of magnitude. [Edit:] A nice consequence of that limit is that 3.16 and 3.14 are almost the same number, so pi sits nicely on the border between this order of magnitude and the next, so you can approximate it as either one or ten, depending on what makes your estimate look better.