# 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?

**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.**

### Guidance

**A percent is a part of a whole. It is a ratio compared to 100.**

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.

**Let’s start by writing percents as decimals and decimals as percents.**

**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.**

**Exactly, and now you might be able to see how we can write percent as a decimal.** They are both comparing to hundreds.

Take a look at this one.

**Write 56% as a decimal.**

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

*Write this down in your notebook.*

**Write 88% as a decimal.**

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

88% = .88

**Write 125% as a decimal.**

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.

**Write .45 as a percent.**

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

.45 = 45%

**Write .345 as a percent.**

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

.345 = 34.5%

*Write this rule down in your notebook.*

Write each example as a decimal or a percent.

#### Example A

\begin{align*}.48\end{align*}

**Solution: \begin{align*}48%\end{align*}**

#### Example B

\begin{align*}57.5%\end{align*}

**Solution:\begin{align*}.575\end{align*}**

#### Example C

\begin{align*}.18\end{align*}

**Solution:\begin{align*}18%\end{align*}**

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

To convert \begin{align*}85%\end{align*} to a decimal, we first drop the percent sign.

\begin{align*}85\end{align*}

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

\begin{align*}.85\end{align*}

**This is our answer.**

### 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 \begin{align*}.455\end{align*} as a percent.

**Solution**

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.

\begin{align*}.455 = 45.5\end{align*}

Now we add a percent sign.

**Our answer is \begin{align*}45.5%\end{align*}.**

### 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.### Image Attributions

## Concept Nodes:

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.