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Decimals as Percents

Rewrite decimals as percents by moving the decimal point.

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Practice Decimals as Percents
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Write Percents as Decimals

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*}0.48\end{align*}

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

Example B

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

Solution:  \begin{align*}0.575\end{align*}

Example C

\begin{align*}0.18\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*}0.85\end{align*}

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*}0.455\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*}.

Practice

Write the following percents as decimals.

1. 18%
2. 35.7%
3. 6.09%
4. .008%
5. .028%
6. .9%
7. 31.5%
8. 12.3%

Write the following decimals as percents.

1. .52
2. .02
3. 1.17
4. 5
5. .09
6. .876
7. .3
8. .0001

Vocabulary Language: English

Decimal

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

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

Proportion

A proportion is an equation that shows two equivalent ratios.