Order of Magnitude

Annotation category:
Chapter 2

ORDER OF MAGNITUDE

The "order of magnitude" of a number is a rough estimate of how big it is. One order of magnitude is a factor of ten.

Two orders of magnitude is: 10 * 10 = a factor of 100. Five orders of magnitude is: 10 * 10 * 10 * 10 * 10 = a factor of 100,000.

   If your checking account is worth $12, and your boss suddenly
   increases it by about two orders of magnitude, you now have
   about $12 * 10 * 10 = $1,200.

   If you have a box containing 200 raisins and you eat 178 of
   them, you have decreased your stash by a factor of
   200/(200-178) = 200/22 = 9.09 = about one order of
   magnitude.

Order-of-magnitude calculations are useful for estimating, either because details are unnecessary for your purposes, or because they are literally impossible to obtain. The number of piano tuners in Manhattan is an example of the former case; the number of stars in the Universe is an example of the latter.