6.10: Small and Large Percents as Decimals
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?
- Drop the % sign.
- 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*}
The answer is 3.5
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*}
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.
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.
Answer
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*}
The answer is .002.
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%