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# 6.10: Small and Large Percents as Decimals

Difficulty Level: At Grade Created by: CK-12
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Practice Small and Large Percents as Decimals

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The largest insect is the Giant Walking Stick, which can be as much as 254,000% the size of the smallest insect, the fairyfly, a member of the wasp family. Conversely, the fairyfly measures a mere 0.03937% the size of the largest Giant Walking Stick. How could you write these percents as decimals?

In this concept, you will learn how to write percents that are less than one and more than 100 as decimals.

### Writing Small and Large Percents as Decimals

Sometimes, you will have a percent that is part of one whole. Such percents will be very tiny.

How would you write the percent 0.5% as a decimal?

This is another way of saying one-half of a percent, or 1%÷2\begin{align*}1\% \div 2\end{align*}. It is therefore smaller than one percent.

You can also have a percent that is greater than one hundred. Such percents are very large—so large, in fact, that they are more than one whole.

300% is one of those percents.

This percent is three times 100 percent, or three wholes.

Let’s look at changing percents like these to decimals.

When converting percents between 1% and 100% to decimals, you:

1. Drop the % sign.
2. Move the decimal point two places to the left. Use zero placeholders as needed.

Now let’s apply these steps to larger and smaller percents.

Let’s try an example.

Write 0.5% as a decimal. First, drop the percent sign.

0.5\begin{align*}0.5\end{align*}

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

0.005\begin{align*}0.005\end{align*}

The answer is 0.5% written as a decimal is 0.005.

Let’s look at another example.

Write 350% as a decimal. First, drop the percent sign. 350

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

3.5\begin{align*}3.5\end{align*}

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

### Examples

#### Example 1

Earlier, you were given a problem about the Giant Walking Stick.

This insect is up to 254,000% the size of the fairyfly. Conversely, the fairyfly is 0.03937% the size of the largest Giant Walking Stick. How could you write these percents as decimals?

Let’s rewrite 254,000% first. First, drop the percent sign.

254,000\begin{align*}254,000\end{align*}

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

2,540.00\begin{align*}2,540.00\end{align*}

You can drop the zeroes after the decimal point because they have no value.

The answer is 254,000% written as a decimal is 2,540.

Now, let’s rewrite 0.03937% as a decimal. First, drop the percent sign.

0.03937\begin{align*}0.03937\end{align*}

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

0.0003937\begin{align*}0.0003937\end{align*}

The answer is 0.03937% written as a decimal is 0.0003937.

#### Example 2

A company that 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 percent as a decimal, simply follow the steps. First, drop the percent sign.

0.02\begin{align*}0.02\end{align*}

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

0.0002\begin{align*}0.0002\end{align*}

The answer is 0.0002 of each shipment is defective.

#### Example 3

Write 0.25% as a decimal. First, drop the percent sign.

0.25\begin{align*}0.25\end{align*}

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

0.0025\begin{align*}0.0025\end{align*}

The answer is 0.25% written as a decimal is 0.0025.

#### Example 4

Write 450% as a decimal. First, drop the percent sign.

450\begin{align*}450\end{align*}

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

4.5\begin{align*}4.5\end{align*}

The answer is 450% written as a decimal is 4.5.

#### Example 5

Write 675% as a decimal. First, drop the percent sign.

675\begin{align*}675\end{align*}

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

6.75\begin{align*}6.75\end{align*}

The answer is 675% written as a decimal is 6.75.

### Review

Rewrite each percent as a decimal.

1. 0.34%
2. 0.5%
3. 350%
4. 650%
5. 0.30%
6. 0.10%
7. 0.09%
8. 0.22%
9. 230%
10. 500%
11. 700%
12. 0.012%
13. 0.04%
14. 0.6%
15. 0.16%

### Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes

### Vocabulary Language: English

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).

Percent

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

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