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# Percents and Decimals

Objective Learn how percents and decimals are related, and how to convert from one to the other.

In this lesson, you will learn a technique for relating decimals to percents. You should realize that the calculations involved in converting decimals to percents are easier, since percents represent ratios that compare a number to 100, and decimals represent fractions with denominators that are powers of 10.

## Expressing a Decimal as a Percent

The following example shows how a proportion can be used to change a decimal to a percent.

Example 1

Convert 0.365 to a percent.

Solution

We need to change the decimal 0.365 to a percent. First express 0.365 as a fraction.

To find the percent, set up and solve a proportion.

 100 Â· 365 = 1,000 Â· x Cross multiply. 36,500 = 1,000 x Divide each side by 1,000. 36.5 = x

## Expressing a Percent as a Decimal

Let's see how to reverse the procedure. In other words, how does one express a percent as a decimal? This change can be accomplished by simply writing the percent as a fraction with 100 as the denominator, and then changing that fraction to a decimal. Here are some good examples.

Example 2

Express 23% as a decimal.

Solution

Write 23% as a fraction with a denominator of 100.

Dividing by 100 results in the movement of the decimal point in the divisor two places to the left. So, . Therefore, 23% = 0.23.

Example 3

Example 4

Computing with percents is an extremely important skill. Be sure to solve numerous problems by yourself. This will help you solidify your understanding of the concept of percent, as well as help with your computational skills involving decimals.

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