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• The concepts for this exercise are summarized below.
  For a complete discussion, read the text.
• Need some basic practice with decimals first?
  Changing Decimals to Fractions
  Multiplying and Dividing Decimals by Powers of Ten

One use for decimals is in working with percents, which are commonplace in everyday life:

• the dress was on sale for [beautiful math coming... please be patient] $\,40\%\,$ off the original price;
• housing costs rose [beautiful math coming... please be patient] $\,5\%\,$ last year;
• there was a [beautiful math coming... please be patient] $\,150\%\,$ increase in telephone activity after the newspaper advertisement.

There are [beautiful math coming... please be patient] $\,100\,$ cents in a dollar.
A century is [beautiful math coming... please be patient] $\,100\,$ years.
The word  percent  means  per one hundred .

The symbol  $\%$  is used for percent.
Whenever you see the symbol   [beautiful math coming... please be patient] $\%$ , you can trade it in for a factor of $\,\frac{1}{100}\,$.
Whenever you see a factor of [beautiful math coming... please be patient] $\,\frac{1}{100}\,$, it can be traded in for a  $\%$  symbol.
This simple idea is the key to success with percents:

Indeed, the symbol  $\%$  even looks a bit like the fraction $\,\frac{1}{100}\,$;
it has the two zeros and the division bar!

To change from a decimal to a percent,
move the decimal point two places to the right and insert the percent symbol.

Here's the idea that makes this work:

[beautiful math coming... please be patient] $\displaystyle 0.03 = \frac{3}{100} = 3\cdot\frac{1}{100} = 3\%$

Notice that the $\displaystyle\,\frac{1}{100}\,$ gets traded in for the percent symbol.