6.3: Percents and Decimals
Introduction
Selling Lollipops
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 the lesson.
What You Will Learn
By the end of this lesson, you will be able to complete the following tasks:
- Write percents as decimals.
- Write decimals as percents.
- Rewrite percents less than one or greater than 100 as decimals.
- Solve real-world problems involving percents less than one or greater than 100.
Teaching Time
I. Write Percents as Decimals
In the last lesson, 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.
How?
Let’s look at the following example and see if we can make better sense of the connection between a decimal and a percent.
Example
.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, it is easy to 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 an example.
Example
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
Example
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
Sometimes you will have a fraction that is a percent. In an example like this, you will have a decimal with a percent sign. We can use the same steps to change those percents to decimals.
Example
Write 35.5% as a decimal.
First, we drop the % sign.
35.5
Next, we move the decimal point two places to the left.
.355
Our answer is .355
6G. Lesson Exercises
Write each percent as a decimal.
- 35%
- 2%
- 18.7%
Take a few minutes to check your work with a friend.
II. Write Decimals as Percents
Just like we can write percents as decimals, we can also write decimals as percents. You saw an example like this in the first section. In a way, you reverse the steps from turning a percent to a decimal to turn a decimal to a percent.
Follow these steps to write a percent as a decimal
Step 1: Move the decimal point two places to the right. Add zeros to the right of the decimal point as placeholders, if necessary.
Step 2: Write a % symbol after the resulting number
Take a few minutes to write these notes in your notebook. Then continue.
Let’s look at how to apply these steps in the following examples.
Example
Write .78 as a percent.
This decimal is written in hundredths, so all we have to do is move the decimal two places to the right and add a percent sign.
\begin{align*}.78 = 78\%\end{align*}
Example
Write .6 as a percent.
This decimal is written in tenths. When we move the decimal two places to the right, we will need to add a zero place holder.
\begin{align*}.6 = 60\%\end{align*}
Example
Write .345 as a percent.
This decimal is written in thousandths. We only need to move the decimal two places to the right to make it a percent, so we will move it two places and add a percent sign.
\begin{align*}.345 = 34.5\%\end{align*}
Example
Write 3.5 as a percent.
This decimal is written with a whole number and five tenths. We still move the decimal to the right two places. Notice that because we have a whole number that the percent will be greater than 100.
\begin{align*}3.5 = 350\%\end{align*}
Notice that sometimes we can have a decimal in a percent. It means that we have 34 and one-half percent in this case. Don’t let that throw you off-not all percents are whole percents!
6H. Lesson Exercises
Write each decimal as a percent.
- .45
- 2.5
- .875
Take a few minutes to check your work with a friend.
III. Rewrite Percents Less than One or Greater than One Hundred as a Decimal
Sometimes, we will have a percent that is part of one whole. These percents are a decimal that is a tiny percent.
Example
.5%
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.
Example
300%
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?
- Drop the % sign.
- Move the decimal point two places to the right. Use zero placeholders as needed.
Example
Write .5% as a decimal.
First, drop the percent sign.
.5
Next, move the decimal point two places to the left.
.005
The answer is .005.
Example
Write 350% as a decimal.
First, drop the percent sign.
350
Next, move the decimal point two places to the left.
3.5
The answer is 3.5
6I. Lesson Exercises
Write each percent as a decimal.
- .25%
- 450%
- 675%
Take a few minutes to check your answers.
IV. Solve Real-World Problems Involving Percents Less than One or Greater than One Hundred
Now let’s apply what we have learned in problem solving. Read each problem carefully and then work on finding each solution.
Example
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.
.02
Next, move the decimal point two places to the left.
.0002
The answer is .0002.
Example
For a science report, Lucas looked up the average rainfall for his town and compared it to the amount of rainfall for the past year. He found that the rainfall last year was 145% of what it is in an average year. Write this percent as a decimal.
First, we write the percentage.
145%
Next, we drop the percent sign.
145
Now move the decimal point two places to the left.
1.45
Our answer is 1.45.
Remember Taylor and the candy store? Let’s think about that problem and use what we have learned to solve it.
Real Life Example Completed
Selling Lollipops
Here is the original problem once again. Reread it and underline any important information.
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 lesson.
- 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.
Technology Integration
Khan Academy Percents and Decimals
James Sousa, Example of Relating Fractions, Decimals, and Percents
James Sousa, Another Example of Relating Fractions, Decimals, and Percents
Other Videos:
- http://www.mathplayground.com/howto_perfracdec.html – This is a video on how to convert fractions/decimals to percents.
Time to 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%
Directions: Write the following decimals as percents.
11. .45
12. .3
13. .675
14. .9
15. .08
16. .785
17. .22
18. .095
19. .54
20. .275
Directions: Write each percent as a decimal.
21. .45%
22. .32%
23. .56%
24. .09%
25. .123%
26. 4.5%
27. 300%
28. 125%
29. 250%
30. 350%