Factorials and Order of Operations

Date: 09/21/2000 at 22:13:18
From: Kiaran D
Subject: Factorials, powers,and Order of Operations

Where do factorials go in the Order of Operations? I've been 
thinking that factorials would go with exponents, but on the other 
hand, factorials go with multiplication.

Date: 09/21/2000 at 22:53:25
From: Doctor Peterson
Subject: Re: Factorials, powers,and Order of Operations

Hi, Kiaran. Good question!

I would put factorials with functions, something you don't often 
see listed in the order of operations. If you are not familiar with 
functions, you can think of them very simply as something to be done 
to a single number (or sometimes a list of numbers) that produces a 
number as a result. The square root and the trigonometric functions 
(sine, cosine) are examples of this. Technically, the factorial is 
called a (postfix) unary operator, which means essentially the same 
thing.

Because these don't stand between two numbers, but only relate to one 
number, they are thought of as being attached directly to that number; 
if you want to apply a function or unary operator to a whole 
expression, you have to use parentheses. That puts functions at the 
top of the order of operations, just after parentheses.

For example, this means that the factorial applies only to the 5:

    3 + 4*5! = 3 + 4*120 = 3 + 480 = 483

while this applies it to (3 + 4*5):

    (3 + 4*5)!

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/