Order of magnitude ($\Delta ={\log }_{10}(x_2/x_1)$)

For positive quantities, a difference of one order of magnitude means a factor of ten; a difference of $n$ orders of magnitude means a factor of $10^n$. The logarithmic difference ${\log }_{10}(x_2/x_1)$ records this comparison, without subtracting the quantities themselves. For example, $1000$ is three orders of magnitude above one, regardless of a common change of units. Roughly assigning a single value to an order of magnitude also requires a rounding convention; powers of ten are the reference levels.