# Percentages

## Warning - Percentages vs. Numbers

Numbers and percentages *are not* interchangeable. Before you can do any calculations with a percentage you have to convert it to a number. This means, for example, that it would be incorrect to say something like 12.5% x 14. The correct procedure would be to convert 12.5 to the equivalent decimal number then multiply that by 14.

Suppose I tell you that one baseball player hit the ball was up to bat 30 times and hit the ball 6 times where another player was at bat 100 times and hit the ball on 25 of them. Which one is the better player? The second player hit the ball more times but he was also up to bat more times. Percentages give us a way to compare these numbers on an equal basis.

The following examples illustrate some common tasks that you'll come across with percentages.

# Converting a Number to a Percentage

**Write .157 as a percentage.**

To convert a number to a percentage you multiply it by 100 so .157 would be equivalent to .157 x 100 = 15.7%.

# Converting a Fraction to a Percentage

**Write 12 / 5 as a percentage.**

This is really the same thing as Example 1 but with a fraction instead of a decimal. The first step in this sort of question is to convert the fraction to its decimal version:

12 / 5 = 1.4

Now you can convert 1.4 to a percentage by multiplying it by 100 just like we did in Example 1: 1.4 x 100 = 140%.

# Converting a Percentage to a Number

**Write 112.6% as a decimal.**

This process is the reverse of what we did in Example 1. To convert a percentage to a number, you *divide* it by 100. This means that 112.6% is equivalent to 112.6 / 100 = 1.126.