# Order of Magnitude

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 = 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.

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