Can order of magnitude be negative?

1 Answer
Nov 21, 2015

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 to 10^3 than to 10^2, so we say that the order of magnitude is 3.

By the same argument, 9.9 × 10^-3 is closer to 10^-2 than to 10^-3, so we say that the order is -3.

In another meaning, it is a difference of 1 unit in the exponent of 10 in the value of a quantity.

Thus, 2315 is one order of magnitude larger than 231.5, and 23.15 is one order of magnitude less than 231.5.

If the value of a number decreased from 2315 to 23.15, 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.