{title2=$\Delta=\log_{10}(x_2/x_1)$}
{wiki}

= Orders of magnitude
{synonym}

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.


 Order of magnitude (source code)