Can order of magnitude be negative?

1 Answer
Nov 21, 2015

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 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.