More generally, I've always wondered with orders-of-magnitude: isn't it misleading to think of, say 2,000 and 9,000 in the same order-of-magnitude?
Shouldn't the test be whether log_10 of the ratio is < 0.5 ? (i.e. ratio is less than √10 ?)
In other words 9,000 and 2,000 are not in the same order of magnitude because their ratio is 4.5.
This does mean that "the same order of magnitude" is not an equivalence relation (it's not transitive) so under the definition above, you can't say "group by order of magnitude".