Orders of Magnitude
Key Questions
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The mathematical explanation is to take the base ten log of a number and floor it, however, that's just a fancy math way of saying count the digits before the decimal marker then take 1.
Lovecraft
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3
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Oct 2 2015
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Answer:
It depends on what you mean by "order of magnitude".
Explanation:
In one meaning, it is a number's nearest power of 10.
For example,
9.9 × 10^2 is much closer to10^3 than to10^2 , so we say that the order of magnitude is3 .By the same argument,
9.9 × 10^-3 is closer to10^-2 than to10^-3 , so we say that the order is-3 .In another meaning, it is a difference of
1 unit in the exponent of10 in the value of a quantity.Thus,
2315 is one order of magnitude larger than231.5 , and23.15 is one order of magnitude less than231.5 .If the value of a number decreased from
2315 to23.15 , we would say that it decreased by two orders of magnitude or that the values differed by two orders of magnitude.In that sense, a difference in orders of magnitude is always expressed as a positive number.
Ernest Z.
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5
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Nov 21 2015