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

2 Answers
Oct 2, 2015

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.

Oct 4, 2015

Answer:

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.