# 6.10: Small and Large Percents as Decimals

Difficulty Level: At Grade Created by: CK-12
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Practice Small and Large Percents as Decimals

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Do you have a favorite color of jelly beans? Sasha loves red ones. Take a look.

Sasha loves jelly beans. In fact, she loves red jelly beans. When Sasha went to the candy store, she looked into a glass jar full of jelly beans and was shocked to discover that there were only a few red ones to be seen.

Because she was curious, Sasha bought a whole bag of the jelly beans.

When she got home, she counted \begin{align*}567\end{align*} jelly beans.

There were only \begin{align*}2\end{align*} red jelly beans in the whole bag.

Sasha wrote 2 out of 567 on a piece of paper.

Sasha wrote down \begin{align*}.3%\end{align*}.

Can you write this as percent as a decimal?

This Concept is about writing percents less than one as a decimal. You will learn how to do this in this Concept.

### Guidance

Sometimes, we will have a percent that is part of one whole. These percents are a decimal that is a tiny percent.

Let's look at one.

\begin{align*}.5%\end{align*}

This is another way of saying \begin{align*}\frac{1}{2}\end{align*} of a percent. It is smaller than one.

We can also have a percent that is greater than one hundred. This is a very large percent-so large that it is larger than one whole.

Here is one of those percents.

\begin{align*}300%\end{align*}

This percent is 300% or three times 100 percent. Wow! That is a large percentage!

Let’s look at changing these percents to decimals.

Think back, remember the steps?

1. Drop the % sign.
2. Move the decimal point two places to the right. Use zero placeholders as needed.

Now let's apply the steps.

Write \begin{align*}.5%\end{align*} as a decimal.

First, drop the percent sign.

\begin{align*}.5\end{align*}

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

\begin{align*}.005\end{align*}

The answer is \begin{align*}.005\end{align*}.

Write \begin{align*}350%\end{align*} as a decimal.

First, drop the percent sign.

\begin{align*}350\end{align*}

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

\begin{align*}3.5\end{align*}

Write each percent as a decimal.

#### Example A

\begin{align*}.25%\end{align*}

Solution:\begin{align*}.0025\end{align*}

#### Example B

\begin{align*}450%\end{align*}

Solution:\begin{align*}4.5\end{align*}

#### Example C

\begin{align*}675%\end{align*}

Solution: \begin{align*}6.75\end{align*}

Here is the original problem once again.

Sasha loves jelly beans. In fact, she loves red jelly beans. When Sasha went to the candy store, she looked into a glass jar full of jelly beans and was shocked to discover that there were only a few red ones to be seen.

Because she was curious, Sasha bought a whole bag of the jelly beans.

When she got home, she counted \begin{align*}567\end{align*} jelly beans.

There were only \begin{align*}2\end{align*} red jelly beans in the whole bag.

Sasha wrote 2 out of 567 on a piece of paper.

Sasha wrote down \begin{align*}.3%\end{align*}.

Can you write this as percent as a decimal?

To write this as a decimal, we can drop the percent sign and move the decimal point two places to the left.

\begin{align*}.3%\end{align*} becomes \begin{align*}.003\end{align*}

### Vocabulary

Here are the vocabulary words in this Concept.

Decimal
a number written according to place value. Numbers to the right of the decimal point represent parts of a whole. Numbers to the left of the decimal point represent whole numbers.
Percent
a part of a whole out of 100. Percents can be smaller than one represented by a decimal percent. They can also be greater than one hundred by having a decimal with a whole number and a part of a whole.

### Guided Practice

Here is one for you to try on your own.

A company which produces light bulbs is very proud of the fact that only 0.02% of each shipment is defective. Write this percent as a decimal.

To write this as a decimal we simply follow the steps. First, drop the percent sign.

\begin{align*}.02\end{align*}

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

\begin{align*}.002\end{align*}

### Practice

Directions: Rewrite each percent as a decimal.

1. .34%

2. .5%

3. 350%

4. 650%

5. .30%

6. .10%

7. .09%

8. .22%

9. 230%

10. 500%

11. 700%

12. .012%

13. .04%

14. .6%

15. .16%

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