**Annotation category:**

Chapter 2

Note: |

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 =aboutone 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.