# 6.8: Percents as Decimals

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

**Practice**Percents as Decimals

Taylor is learning a lot about money from working in the candy store. Her Dad took out a ledger one day to show Taylor how he keeps track of which candies are selling and which ones aren’t. He also keeps track of the sales of candy each month to figure out how much to reorder.

Last month, lollipops were the big hit. Taylor’s Dad put out 500 lollipops on the first of the month and they sold all 500 during the course of the month.

“Last month we sold 100% of the lollipops, I put out 750 this month,” he told her.

As the month went on, Taylor noticed that the lollipops were selling just as well as they had the month before. At the end of the month her Dad wrote down the statistics in his ledger.

“We sold all 750 plus another 25%,” Taylor’s Dad told her.

Taylor thought about this. Wow! That is a lot of lollipops.

Taylor began thinking about the sales in terms of percents.

100% of the lollipops were sold.

Plus they sold an additional 25%

What is the total percentage sold? How can a percent be greater than 100? What would this be as a decimal?

**As Taylor grapples with these questions, you can too. You will be able to figure this out at the end of this Concept.**

### Guidance

In an earlier Concept, you were able to see the connection between fractions and percents. Well, decimals also represent a part of a whole just like fractions and percents. Therefore, you can 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 will also keep track of the place value.

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

**How?**

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

.52

**This decimal states that we have 52 hundredths, Wow! There is the connection right there. The percent sign means “out of 100” so we have 52 hundredths or we have 52 parts out of 100.**

**Once you see the connection, then we can write this as a percent.**

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

**Both mean that we have 52 parts out of 100.**

**That is a very good question!** If you look at the conversion carefully, you can see that we moved the decimal point two places to the right. Why? We did that because we want to show hundredths. Percent is out of 100, so the % sign is the same as the two decimal places.

**Now that you see the connection, let’s look at how we do this.**

**How do we write a percent as a decimal?**

**Here are the steps:**

**Step 1:** Drop the % symbol.

**Step 2:** Move the decimal point two places to the left. Add zeros to the right of the decimal point as placeholders, if necessary.

*Take a few minutes to write these steps in your notebook.*

Now let’s look at another one.

Write 25% as a decimal.

**First, we drop the % sign.**

25

**Next, we move the decimal point two places to the left. This is the hundredths place remember that two places is hundredths. We just dropped the percent sign which means out of 100 so we have to put that into our answer.**

**.25**

**Our answer is .25**

Write 9% as a decimal.

**First, we drop the % sign.**

9

**Next, we move the decimal point two places to the left. Because nine is only one digit we have add a place holder zero to show the two decimal places.**

.09

**Our answer is .09**

Now it's time for you to try a few on your own. Write each percent as a decimal.

#### Example A

\begin{align*}35%\end{align*}

**Solution:\begin{align*}.35\end{align*}**

#### Example B

\begin{align*}2%\end{align*}

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

#### Example C

\begin{align*}18.7%\end{align*}

**Solution:\begin{align*}.187\end{align*}**

Here is the original problem once again.

Taylor is learning a lot about money from working in the candy store. Her Dad took out a ledger one day to show Taylor how he keeps track of which candies are selling and which ones aren’t. He also keeps track of the sales of candy each month to figure out how much to reorder.

Last month, lollipops were the big hit. Taylor’s Dad put out 500 lollipops on the first of the month and they sold all 500 during the course of the month.

“Last month we sold 100% of the lollipops, I put out 750 this month,” he told her.

As the month went on, Taylor noticed that the lollipops were selling just as well as they had the month before. At the end of the month her Dad wrote down the statistics in his ledger.

"We sold all 750 plus another 25%,” Taylor’s Dad told her.

Taylor thought about this. Wow! That is a lot of lollipops.

Taylor began thinking about the sales in terms of percents.

100% of the lollipops were sold.

Plus they sold an additional 25%

What is the total percentage sold? How can a percent be greater than 100? What would this be as a decimal?

**First, let’s figure out the total percentage of lollipops sold.**

**100% + 25% = 125% of the lollipops were sold.**

**It may seem strange that numbers can be over 100%, but in the case of the lollipops you can understand how this happens. They sold all that they had put out and then put out even more lollipops. This happens in sales all the time. Sales are often increased over 100%. This is a very good thing for business.**

**How is this written as a decimal?**

**125% = _______**

**First, drop the percent sign.**

**125**

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

**1.25**

**This is the answer.**

### 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.

Write 35.5% as a decimal.

**Answer**

First, we drop the % sign.

\begin{align*}35.5\end{align*}

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

\begin{align*}.355\end{align*}

**Our answer is \begin{align*}.355\end{align*}.**

### Video Review

Here is a video for review.

- This James Sousa video relates fractions, decimals and percents.

### Practice

Directions: Write the following percents as decimals.

1. 12%

2. 15%

3. 3%

4. 67%

5. 18%

6. 78%

7. 34%

8. 7%

9. 3%

10. 34%

11. 18%

12. 33.5%

13. 18.5%

14. 13.25%

15. 6.75%

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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).