# 5.2: Write Percents as Decimals

**At Grade**Created by: CK-12

**Practice**Decimals as Percents

Have you ever wondered how a percent could be a decimal? Take a look at this dilemma.

Karen earned 85% on a math test. She wondered how she could show this as a decimal. Do you know?

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This Concept will show you how to write decimals as percents and percents as decimals. Then you will know how to tackle this problem at the end of the Concept.
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### Guidance

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A percent is a part of a whole. It is a ratio compared to 100.
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Fractions and decimals are parts of a whole too. If this is true, then we can interchange the form that we write these quantities in. We can write a fraction as a decimal and as a percent. We can also write a percent as a decimal or a decimal as a percent and we can do the same with the fractions too.

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Let’s start by writing percents as decimals and decimals as percents.
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We can start by thinking about decimals. Decimal places represent powers of ten. The second decimal place is the hundredths place. The decimal .18 means eighteen-hundredths.
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Exactly, and now you might be able to see how we can write percent as a decimal.
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They are both comparing to hundreds.

Take a look at this one.

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Write 56% as a decimal.
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To do this, we know that the % sign means “out of 100” we can say that decimal places represent tens and hundreds too. Two decimal places represents hundreds, just like the percent sign, %, represents hundreds.

To change a percent to a decimal, we drop the percent sign and move the decimal point two places to the left.

56% = .56

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Write this down in your notebook.
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Write 88% as a decimal.
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To do this, we drop the percent sign and move the decimal point two places to the left.

88% = .88

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Write 125% as a decimal.
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Even though this percent is greater than 100, we still follow the same steps.

125% = 1.25

We can work the other way around too and write decimals as percents. Here we will move the decimal point two places to the right and add a percent sign.

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Write .45 as a percent.
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First, we move the decimal point two places to the right and add a percent sign.

.45 = 45%

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Write .345 as a percent.
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Follow the same rule here. Just move the decimal point two places to the right and add a percent sign.

.345 = 34.5%

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Write this rule down in your notebook.
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Write each example as a decimal or a percent.

#### Example A

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Solution:
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#### Example B

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Solution:
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#### Example C

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Solution:
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Now let's go back to the dilemma from the beginning of the Concept.

To convert to a decimal, we first drop the percent sign.

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

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This is our answer.
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### Vocabulary

- Ratio
- a comparison between two quantities.

- Percent
- a ratio that is being compared to the quantity of 100. Percent means out of 100.

- Fraction
- a part of a whole written using a numerator and a denominator.

- Decimal
- a part of a whole written in base ten place value.

- Proportion
- two equal ratios form a proportion.

### Guided Practice

Here is one for you to try on your own.

Write as a percent.

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Solution
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When converting a decimal to a percent, we move the decimal point two places to the right. This represents the hundredths that are shown with a percent sign.

Now we add a percent sign.

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Our answer is
.
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### Video Review

### Practice

Write the following percents as decimals.

- 18%
- 35.7%
- 6.09%
- .008%
- .028%
- .9%
- 31.5%
- 12.3%

Write the following decimals as percents.

- .52
- .02
- 1.17
- 5
- .09
- .876
- .3
- .0001

Decimal

In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).Percent

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

A proportion is an equation that shows two equivalent ratios.