Question

How do I find the order of magnitude of a number?

Answer 1

The mathematical explanation is to take the base ten log of a number and floor it, however, that's just a fancy math way of saying count the digits before the decimal marker then take 1.

Answer 2

Orders of magnitude are approximately common logarithms of ratios of numbers, typically rounded to the nearest integer below.

If your number already represents a ratio, then take its common log.

Explanation:

If one number is `10` times another, then we can say that it is an order of magnitude larger.

Orders of magnitude represent a comparison of scale, for example, `1"kg"` is three orders of magnitude larger than `1"g"`

The "order of magnitude of `500`" is meaningless except in comparison to another number. The order of magnitude of the ratio `500:1` is meaningful, typically by saying that one thing is `2` orders of magnitude larger than another thing.

Note that orders of magnitude try not to exaggerate the scale, choosing to express that `500/1 > 10^2` rather than the fact that `log(500) ~~ 2.69897` so `500/1 ~~ 10^2.69897`

If we are faced with a ratio like `900:1`, then we would probably say that something was "roughly three orders of magnitude larger than" another thing.