Question

Can order of magnitude be negative?

Answer 1

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.