> I was hoping "roughly speaking an order of magnitude" would go down to 3.

I'd call that half a order of magnitude, considering log₁₀(3) is around 0.477. So you're off by more than a factor of two.

You know, I considered saying that the "roughly" buys me a factor of two in log space. I didn't want to be that person, but I'm glad you were ;).

It's surprisingly non-trivial to pin down exactly what the 'correct' scale[0] for a given measurement is. I do agree about "roughly" generally being up to a factor of two in the appropriate scale[1], although I'm the sort who thinks a 19% increase (or 16% decrease) should be called a quarter of a factor of two.

0: Uniform, linear and logarithmic are obvious candidates, but depending on the domain you can end up with some really wierd scales (eg floating-point ULPs, which can look logarithmic or linear, but aren't either).

1: hence > So you're off by more than a factor of two.

3 is half an order of magnitude (because it is a good approximation to 10^0.5)

re go down to 3: Use different words and see if you think it was reasonable

roughly 10x going down to 3x would also mean it would go up to 17x. That's a pretty wide range, so I don't think that order of magnitude is going to ever really be similar to 3x of something on the basis of what it means.

but what about a rough order of magnitude? There is definitely some qualifiers you can put on "order of magnitude" to make it include 3.

"within an order of magnitude"