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.

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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".