Converting between fractions, decimals, and percents

Rules for converting between fractions, decimals, and percents

In this lesson you will learn how to convert between fractions, decimals and percents.

You can always use a proportion to help you convert from fractions, decimals and percents.

$\frac{\text{percent}}{100}=\frac{\text{part}}{\text{whole}}$

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You can also use these rules:

1. A percent means some indicated part out of $100$. For instance, $4\%$ means $4$ out of every $100$.

2. To change a percent to a decimal, divide by $100$. For instance, to change $49\%$ to a decimal, divide it by $100$.

$49\%=\frac{49}{100}=0.49$

3. To change a decimal to a percent, multiply by $100$. For instance, to change $0.05$ to a percent, multiply it by $100$.

$0.05 \cdot 100 = 5\%$

4. To change a fraction to a percent, first change the fraction to a decimal, then change the decimal to a percent. For instance, to change $1/4$ to a percent, first change it to $0.25$, and then multiply $0.25$ by $100$ to get the percent.

$\frac{1}{4} = 0.25$

$0.25 \cdot 100 = 25\%$

5. To find a percent of a number in decimal form, change the percent to a decimal and multiply it by that number. For instance, to find $6\%$ of $99$, convert $6\%$ to a decimal by dividing by $100$.

$\frac{6}{100}=0.06$

Then multiply $0.06$ by $99$.

$0.06 \cdot 99 = 5.94$

$6\%$ of $99$ is $5.94$

Converting between fractions, decimals, and percents

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Changing a percent into a mixed fraction

Example

Find a mixed fraction that represents the given value.

$9\%$ of $160$

To find $9\%$ of $160$, we set it up as

$\frac{9}{100} \cdot 160$

$\frac{9}{5} \cdot 8$

$\frac{72}{5}$

$5$ goes into $72$ fourteen times, with a remainder of $2$, so we can change the improper fraction to a mixed fraction and get

$14\frac{2}{5}$

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Let’s look at one more example of converting fractions to percents.

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To change a fraction to a percent, first change the fraction to a decimal, then change the decimal to a percent.

Example

Convert the fraction to a percent.

$\frac{120}{180}$

First, since the fraction isn’t already in lowest terms, we’ll reduce it to lowest terms.

$\frac{120 \div 60}{180 \div 60}$

$\frac{2}{3}$

One way we can convert this fraction to a percent is to first convert it to a decimal using long division, and then convert the decimal to a percent by moving the decimal place, or we can set up the proportion

$\frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100}$

and use the variable $x$ for the missing piece (the percent).

$\frac{2}{3} = \frac{x}{100}$

$2 \cdot 100 = 3x$

$200 = 3x$

$\frac{200}{3}$ $= 66.66...$

You could round a repeating decimal to an indicated decimal place. For example, if you round $66.66...$ to the hundredths place (round it to two decimal places), you’ll get $66.67\%$.

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