If we go by log10 of the number, 4 would be enough to round up to "10" as an order of magnitude.
That just doesn't seem right to me, though. My non-rigorous intuition would put the cutoff at 7.
That just doesn't seem right to me, though. My non-rigorous intuition would put the cutoff at 7.
[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.
Gets weird thinking about 9 being both one number less and one order of magnitude less than 10, while 99 is both 89 more and the same order of magnitude, but it's supposed to be a rough approximation.