Okay so I’m just going to open myself up to ridicule here; my understanding of comparing numbers using orders of magnitude might be wrong, and if it is, I would like to know that. So on that note, I don’t think that’s how OOM comparisons work, and I’d be very interested to be corrected if I’m wrong.
You could accurately say that 2.1B has 2 more orders of magnitude than 73M does (7 vs. 9), but I believe when you’re directly comparing two numbers and saying that one is “x orders of magnitude larger than y”, that doesn’t work. You wouldn’t say that 10 is an order of magnitude larger than 9… that would be very misleading; 90 is an order of magnitude larger than 9. In fact, that claim would be off by… approximately an order of magnitude.
1 order of magnitude larger than 73M is 730M; 2 orders of magnitude larger is 7.3B, as you note, but… wouldn’t you look upward to say a number is in the same order of magnitude, not lower? So since 2.1B is approximately 29x larger than 73M, it would be 1 OOM larger (and only becomes 2 OOM larger at 100x)?
To look at it another way:
73M x 10^1 is a lot closer to the correct value than 73M x 10^2, so even if the correct method is to round to the nearest OOM, it wouldn’t beecome 2 OOM larger until 73M x 50, or 3.650B.
Again, it’s quite possible that my understanding is incorrect because… this doesn’t come up in every day conversation much, so if I’m wrong, please correct me!
Okay so I’m just going to open myself up to ridicule here; my understanding of comparing numbers using orders of magnitude might be wrong, and if it is, I would like to know that. So on that note, I don’t think that’s how OOM comparisons work, and I’d be very interested to be corrected if I’m wrong.
You could accurately say that 2.1B has 2 more orders of magnitude than 73M does (7 vs. 9), but I believe when you’re directly comparing two numbers and saying that one is “x orders of magnitude larger than y”, that doesn’t work. You wouldn’t say that 10 is an order of magnitude larger than 9… that would be very misleading; 90 is an order of magnitude larger than 9. In fact, that claim would be off by… approximately an order of magnitude.
1 order of magnitude larger than 73M is 730M; 2 orders of magnitude larger is 7.3B, as you note, but… wouldn’t you look upward to say a number is in the same order of magnitude, not lower? So since 2.1B is approximately 29x larger than 73M, it would be 1 OOM larger (and only becomes 2 OOM larger at 100x)?
To look at it another way:
73M x 10^1 is a lot closer to the correct value than 73M x 10^2, so even if the correct method is to round to the nearest OOM, it wouldn’t beecome 2 OOM larger until 73M x 50, or 3.650B.
Again, it’s quite possible that my understanding is incorrect because… this doesn’t come up in every day conversation much, so if I’m wrong, please correct me!