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It is ten times. This is used a lot by scientists where numbers can be very different from each other. For example Jupiter have a mass of roughly 10^(27) kg while the Sun have a mass of roughly 10^(30) kg. So we say that the Sun is three orders of magnitude larger then Jupiter.
number of digits.
so 1 and 10 are 1 order of magnitude appart since 10 has 1 more digit than 1.
10000 and 20 are 3 orders of magnitude different.
etc.
since the difference is so big, it doesnt really matter if we are talking about 20 or 30, its still 3 orders of magnitude.
mathematically it is round(|log_10(a)-log_10(b)|), but you can easily free-hand it without messing with logs, and its gennerally just an approximation
A power of 10
Let’s say I’m doing a math problem and the answer is 5000 and I get the answer 500. I’m off by an order of magnitude
If I’m doing a calculation and I just want a rough estimate, I could do all the calculations with just powers of 10, then my end result will be the same order of magnitude as the answer. So if I’m looking for an answer on the order of 10^30 and then someone gives a more precise answer of 2.2×10^25 then one of us made an error because our answers are off by 5 orders of magnitude
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