To convert a decimal to a percent, remember that percent means per hundred. If we change the decimal to a fraction whose denominator is [latex]100[/latex], it is easy to change that fraction to a percent.
example
Convert each decimal to a percent:
ⓐ [latex]0.05[/latex] ⓑ [latex]0.83[/latex]
Solution
| ⓐ |
|
|
[latex]0.05[/latex] |
| Write as a fraction. The denominator is [latex]100[/latex]. |
[latex]\frac{5}{100}[/latex] |
| Write this ratio as a percent. |
[latex]5[/latex]% |
| ⓑ |
|
|
[latex]0.83[/latex] |
| The denominator is [latex]100[/latex]. |
[latex]\frac{83}{100}[/latex] |
| Write this ratio as a percent. |
[latex]83[/latex]% |
example
Convert each decimal to a percent:
ⓐ [latex]1.05[/latex] ⓑ [latex]0.075[/latex]
Answer:
Solution
| ⓐ |
|
|
[latex]0.05[/latex] |
| Write as a fraction. |
[latex]1\frac{5}{100}[/latex] |
| Write as an improper fraction. The denominator is [latex]100[/latex]. |
[latex]\frac{105}{100}[/latex] |
| Write this ratio as a percent. |
[latex]105[/latex]% |
Notice that since [latex]1.05>1[/latex], the result is more than [latex]\text{100%.}[/latex]
| ⓑ |
|
|
[latex]0.075[/latex] |
| Write as a fraction. The denominator is [latex]1,000[/latex]. |
[latex]\frac{75}{1,000}[/latex] |
| Divide the numerator and denominator by [latex]10[/latex], so that the denominator is [latex]100[/latex]. |
[latex]\frac{7.5}{100}[/latex] |
| Write this ratio as a percent. |
[latex]7.5[/latex]% |
example
Convert each fraction or mixed number to a percent:
ⓐ [latex]\frac{3}{4}[/latex] ⓑ [latex]\frac{11}{8}[/latex] ⓒ [latex]2\frac{1}{5}[/latex]
Answer:
Solution
To convert a fraction to a decimal, divide the numerator by the denominator.
| ⓐ |
[latex]\frac{3}{4}[/latex] |
| Change to a decimal. |
 |
| Write as a percent by moving the decimal two places. |
[latex]75[/latex]% |
| ⓑ |
[latex]\frac{11}{8}[/latex] |
| Change to a decimal. |
 |
| Write as a percent by moving the decimal two places. |
[latex]137.5[/latex]% |
| ⓒ |
[latex]2\frac{1}{5}[/latex] |
| Write as an improper fraction. |
[latex]\frac{11}{5}[/latex] |
| Change to a decimal. |
 |
| Write as a percent. |
[latex]220[/latex]% |
Convert [latex]\frac{5}{7}[/latex] to a percent.
Answer:
Solution
To change a fraction to a decimal, we divide the numerator by the denominator.
|
[latex]\frac{5}{7}[/latex] |
| Change to a decimal—rounding to the nearest thousandth. |
[latex]0.714[/latex] |
| Write as a percent. |
[latex]71.4[/latex]% |
Notice that we needed to add zeros at the end of the number when moving the decimal two places to the right.
Sometimes when changing a fraction to a decimal, the division continues for many decimal places and we will round off the quotient. The number of decimal places we round to will depend on the situation. If the decimal involves money, we round to the hundredths place. For most other cases in this book we will round the number to the nearest thousandth, so the percent will be rounded to the nearest tenth.
To summarize, here are the results from the previous example in a table.
In Decimals, we learned how to convert fractions to decimals. Now we also know how to change decimals to percents. So to convert a fraction to a percent, we first change it to a decimal and then convert that decimal to a percent.
