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# Decimals as Percents

## Rewrite decimals as percents by moving the decimal point.

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Decimals as Percents

Remember Sam and the sweeping dilemma? Well, Sam wrote fractions as percents, but she could also have used decimals.

What would this have looked like?

Here is the problem from the last Concept.

Sam’s least favorite part of her afterschool job at the supermarket is closing. When closing the store, the break room has to be swept and mopped. Each of the students who work at the store part-time take turns closing, and every Friday night is Sam’s turn. On Friday, Sam got her mop and broom and headed up to the break room. It seemed to be even messier than usual. “Oh no, I will never get done,” Sam sighed, but she picked up the broom and began to sweep.

In just fifteen minutes, Sam had swept four-fifths of the room. She was amazed at how quickly the task was getting done with a little focus and effort.

How could we write this fraction as a decimal?

How could we write the fraction of the room left to clean as a decimal?

In this Concept, you will learn all about converting decimals to percents.

### Guidance

In an earlier Concept, you learned to convert percents to decimals.

Write \begin{align*}31%\end{align*} as a decimal.

You will recall that to do this, we drop the % sign and move the decimal point two places in to the left. These two places represent the hundredths place of the decimal.

\begin{align*}31%\end{align*} becomes \begin{align*}.31\end{align*}

Our answer is \begin{align*}.31\end{align*}.

We can also write a decimal as a percent. To do this, we are going to move the decimal point two places to the right and add a percent sign.

Write \begin{align*}.14\end{align*} as a percent.

To do this, we move the decimal point two places to the right because two decimal places represent hundredths and percents are out of 100. Then we add in the % sign.

Sometimes, you will have a decimal that is written with a zero for the tenths place. We do the same thing to convert to a percent. Move the decimal two places to the right and add a percent sign.

Write \begin{align*}.03\end{align*} as a percent.

\begin{align*}.03\end{align*} becomes \begin{align*}3%\end{align*}

What about a decimal that does not have two decimal places represented?

Write \begin{align*}.2\end{align*} as a percent.

To do this, we move the decimal point two places to the right, which will require adding a zero. Then we can see that two tenths becomes 20 percent.

What about if you have a decimal with more than two places?

When this happens, it is an interesting case, because you have to move the decimal point two places to the right, but you will have a percent that is also a decimal.

\begin{align*}.345\end{align*}

\begin{align*}.345\end{align*} becomes \begin{align*}34.5%\end{align*}.

Now it is time for you to practice. Write each decimal as a percent.

#### Example A

\begin{align*}.85\end{align*}

Solution:\begin{align*}85%\end{align*}

#### Example B

\begin{align*}.09\end{align*}

Solution: \begin{align*}9%\end{align*}

#### Example C

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

Solution:\begin{align*}50%\end{align*}

Now let's go back to Sam and her sweeping. Here is the original problem.

Sam’s least favorite part of her after school job at the supermarket is closing. When closing the store, the break room has to be swept and mopped. Each of the students who work at the store part-time take turns closing, and every Friday night is Sam’s turn. On Friday, Sam got her mop and broom and headed up to the break room. It seemed to be even messier than usual.

“Oh no, I will never get done,” Sam sighed, but she picked up the broom and began to sweep.

In just fifteen minutes, Sam had swept four-fifths of the room. She was amazed at how quickly the task was getting done with a little focus and effort.

How could we write this fraction as a decimal?

How could we write the fraction of the room left to clean as a decimal?

Sam had swept four - fifths of the room. We can convert four - fifths to a decimal. First, let's write it as a proportion.

\begin{align*} \frac{4}{5} = \frac{x}{100}\end{align*}

Now we can solve the proportion.

\begin{align*} \frac{80}{100}\end{align*}

The decimal is \begin{align*}.80\end{align*}.

Now we can use mental math to figure out the decimal of the room that she has left to sweep.

Sam has \begin{align*}.20\end{align*} left to sweep.

### Vocabulary

Here are the vocabulary words in this Concept.

Percent
is "per-cent" or "per-hundred", it is a quantity written with a % sign, a part of a whole (100)
Fraction
a part of a whole, related to decimals and percents.
Decimal
a part of a whole shown by a decimal point, hundredths means two decimal places.
Equivalent
means equal

### Guided Practice

Here is one for you to try on your own.

What is \begin{align*}.009\end{align*} as a percent?

To convert a decimal to a percent, we move the decimal point two places to the right and add a percent sign.

### Video Review

Here are videos for review.

### Practice

Directions: Write each decimal as a percent.

1. .31

2. .56

3. .43

4. .08

5. .01

6. .4

7. .6

8. .65

9. .33

10. .19

11. .3

12. .9

13. .11

14. .18

15. .34

16. .99

17. .21

18. .88

### 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).
Equivalent

Equivalent

Equivalent means equal in value or meaning.
fraction

fraction

A fraction is a part of a whole. A fraction is written mathematically as one value on top of another, separated by a fraction bar. It is also called a rational number.
Percent

Percent

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