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# Decimals as Percents

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

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Decimals as Percents

Jessica’s New Year’s resolution is to run one mile on her treadmill every day. On a random day in January, her treadmill readout shows that she ran 2.9 miles. What percent of her running goal did she achieve that day?

In this concept, you will learn how to write decimals as percents.

### Writing Decimals as Percents

You can write percents as decimals, and you can also write decimals as percents.

First, move the decimal point two places to the right. Add zeros to the right of the decimal point as placeholders, if necessary.

Then, write a % symbol after the resulting number.

Let’s apply these steps to an example.

Write 0.78 as a percent.

This decimal is already written in hundredths because there are two digits after the decimal point. All you have to do is move the decimal two places to the right and add a percent sign.

\begin{align*}0.78 = 78 \%\end{align*}

The answer is 0.78 written as a percent is 78%.

Let’s try another example.

Write 0.345 as a percent.

This decimal is written in thousandths because there are three digits after the decimal point. You only need to move the decimal point two places to the right to make it a percent, so you will have a digit left over that remains after the decimal point.

\begin{align*}0.345 = 34.5 \%\end{align*}

The answer is 0.345 written as a percent is 34.5%.

Notice that sometimes you can have a decimal in a percent. In this case, it means that you have 34 and one-half percent. Not all percents are whole percents.

Let’s try one more example.

Write 3.5 as a percent.

This decimal is written with a whole number and five tenths. You still move the decimal point to the right two places, adding a zero as a placeholder. Notice that because you have a whole number in front of the decimal point that the percent will be greater than 100.

\begin{align*}3.5 = 350 \%\end{align*}

The answer is 3.5 written as a percent is 350%.

### Examples

#### Example 1

Earlier, you were given a problem about Jessica and her New Year’s resolution.

One day in January her treadmill readout recorded that she ran 2.9 miles. What percent of her 1-mile running goal did she achieve that day?

This decimal is written with a whole number and nine tenths.

First, move the decimal point to the right two places.

Then, notice that because you have a whole number in front of the decimal point that the percent will be greater than 100.

\begin{align*}2.9 = 290 \% \end{align*}

The answer is Jessica ran 290% of her 1-mile goal that day.

#### Example 2

Write 0.6 as a percent.

This decimal is written in tenths because there is only one digit after the decimal point. When you move the decimal two places to the right, you will therefore need to add a zero placeholder.

\begin{align*}0.6 = 60 \%\end{align*}

The answer is 0.6 written as a percent is 60%.

#### Example 3

Write 0.45 as a percent.

This decimal is already written in hundredths because there are two digits after the decimal point. Therefore, all you have to do is move the decimal two places to the right and add a percent sign.

\begin{align*}0.45 = 45 \%\end{align*}

The answer is 0.45 written as a percent is 45%.

#### Example 4

Write 2.5 as a percent.

This decimal is written with a whole number and five tenths. You still move the decimal point to the right two places, adding a zero as a placeholder. Notice that because you have a whole number in front of the decimal point that the percent will be greater than 100.

\begin{align*}2.5 = 250 \% \end{align*}

The answer is 2.5 written as a percent is 250%.

#### Example 5

Write 0.875 as a percent.

This decimal is written in thousandths because there are three digits after the decimal point. You only need to move the decimal point two places to the right to make it a percent, so you will have a digit left over that remains after the decimal point.

\begin{align*}0.875 = 87.5 \%\end{align*}

The answer is 0.875 written as a percent is 87.5%.

### Review

Write the following decimals as percents.

1. 0.45
2. 0.3
3. 0.675
4. 0.9
5. 0.08
6. 0.785
7. 0.22
8. 0.095
9. 0.54
10. 0.275
11. 0.04
12. 0.045
13. 0.112
14. 4.6
15. 0.672

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### Vocabulary Language: English

TermDefinition
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).