# Factorials and Absolute Values

Most mathematical operators are written *between* the two numbers they operate on, or *before *the number if it operates on only one number (like the minus sign used as a unary operator). But factorials and absolute values are two mathematical operators that appear in typeset expressions in peculiar ways.

## Factorials

Lots of statistical formulas contain exclamation points (!). An exclamation point doesn't mean that you should sound excited when you read the formula aloud. An exclamation point *after* a number is shorthand for calculating that number's *factorial.*

To find a number's factorial, you write all the whole numbers from 1 to that number and then multiply them all together. For example, 5! (read as "five factorial") is shorthand for 1 × 2 × 3 × 4 × 5, which you can work out on your calculator to get the value 120.

Even though standard keyboards have a ! key, most computer programs and spreadsheets don't let you use ! to indicate factorials; you may have to write it as FACT(5), Factorial(5), or something similar, instead of 5!

Here are a few factorials fun facts:

Factorials grow

**very fast**: You can calculate that 10! is 3,628,800. And 170! is about 7.3 x 10^{306}, which is close to the largest numbers many computers can deal with.0! isn't 0, but is actually 1 (the same as 1!). That may not make any sense, but that's how it is, so burn it into your memory.

The definition of

*factorial*can be extended to fractions and even to negative numbers. Fortunately, you don't have to deal with factorials of fractional numbers in this book.

## Absolute values

The *absolute value* is just the value of the number without any minus sign (if it was negative in the first place). Indicate absolute value by placing vertical bars immediately to the left and right of the number. So |5.7| is 5.7, and |–5.7| is also 5.7. Even though most keyboards have the | symbol, the absolute value is usually indicated in plain text formulas as abs(5.7).