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Percents as Decimals

Rewrite percents as decimals.

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Percents as Decimals
License: CC BY-NC 3.0

A survey was conducted in 2014 to determine what percent of their income Americans give to charity. The responses to the survey revealed that Americans give 4.2% of their gross income to charity. That means that 95.8% of their gross income is not given to charity. How could you write these two percentages as decimals?

In this concept, you will learn to write percents as decimals.

Writing Percents as Decimals

Decimals represent a part of a whole just like fractions and percents do. You are able to write fractions as percents and percents as fractions. You can also convert a decimal to a percent and a percent back to a decimal again.

A decimal organizes numbers according to place value. When you write a decimal as a percent, you also keep track of the place value.

A percent is a part of a whole out of 100. Well, so is a decimal.

Let’s see if you can make better sense of the connection between a decimal and a percent.

0.52

This decimal states that you have 52 hundredths. The percent sign means “out of 100” so you have 52 hundredths or 52 parts out of 100.

Once you see the connection, you can write this and all decimals as a percent.

\begin{align*}0.52 = 52\%\end{align*}

Both mean that you have 52 parts out of 100.

You move the decimal point two places to the right to show hundredths. Percent is “out of 100,” so the % sign is the same as two decimal places: \begin{align*}0.52 \times 100 = 52\end{align*}.

Let’s look at how you write any percent as a decimal.

First, drop the % symbol.

Then, move the decimal point two places to the left.

Finally, add zeros to the right of the decimal point as placeholders, if necessary.

Let’s take a look at another example.

Write 9% as a decimal. First, drop the % sign.

9

Next, move the decimal point two places to the left. Because 9 is only one digit, you have to add a placeholder zero to show the two decimal places.

0.09

The answer is 9% written as a decimal is 0.09.

Let’s look at one final example.

Write 35.5% as a decimal.

First, drop the % sign. 35.5

Next, move the decimal point two places to the left.

0.355

The answer is written as a decimal, 35.5% is 0.355.

Examples

Example 1

Earlier, you were given a problem about the charitable giving survey.

In 2014, it was determined that Americans give 4.2% of their gross income to charity. That means they do not give 95.8% of their income to charity. How would you write each of these percents as a decimal?

First, let’s work with 4.2%. Drop the % sign.

4.2

Next, move the decimal point two places to the left. Because 4 is only one digit, you have to add a placeholder zero to show the two decimal places.

0.042

The answer is 4.2% written as a decimal is 0.042.

Now let’s work with 95.8%.

First, drop the % sign.

95.8

Next, move the decimal point two places to the left.

0.958

The answer is 95.8% written as a decimal is 0.958.

Example 2

Write 25% as a decimal.

First, drop the % sign.

25

Although you can’t see it, the decimal point falls immediately to the right of any whole number.

Next, move the decimal point two places to the left. This is the hundredths place. Remember that two places is hundredths. You just dropped the percent sign, which means out of 100, so your answer has to reflect “out of 100” in a different way.

0.25 The answer is 25% written as a decimal is 0.25.

Example 3

What is 35% written as a decimal?

First, drop the % sign.

35

Next, move the decimal point two places to the left.

0.35

The answer is 35% written as a decimal is 0.35.

Example 4

What is 2% written as a decimal?

First, drop the % sign.
2

Next, move the decimal point two places to the left. Because 2 is only one digit, you have to add a placeholder zero to show the two decimal places.

0.02

The answer is 2% written as a decimal is 0.02.

Example 5

What is 18.7% written as a decimal?

First, drop the % sign.

18.7

Next, move the decimal point two places to the left.

0.187

The answer is 18.7% written as a decimal is 0.187.

Review

Write the following percents as decimals.

  1. 12%
  2. 15%
  3. 3%
  4. 67%
  5. 18%
  6. 78%
  7. 34%
  8. 7%
  9. 6%
  10. 36%
  11. 28%
  12. 33.5%
  13. 18.5%
  14. 13.25%
  15. 6.75%

Review (Answers)

To see the Review answers, open this PDF file and look for section 6.8.

Resources

 

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Vocabulary

Percent

Percent means out of 100. It is a quantity written with a % sign.

Image Attributions

  1. [1]^ License: CC BY-NC 3.0

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