6.1 Understand percent  (Page 4/6)

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.

Convert each fraction or mixed number to a percent: ⓐ $\frac{3}{4}$ ⓑ $\frac{11}{8}$ ⓒ $2\frac{1}{5}$

Solution

To convert a fraction to a decimal, divide the numerator by the denominator.

ⓐ
Change to a decimal.	$\frac{3}{4}$
Write as a percent by moving the decimal two places.
	$\mathrm{75\%}$

ⓑ
Change to a decimal.	$\frac{11}{8}$
Write as a percent by moving the decimal two places.
	$\mathrm{137.5\%}$

ⓒ
Write as an improper fraction.	$2\frac{1}{5}$
Change to a decimal.	$\frac{11}{5}$
Write as a percent.
	$\mathrm{220\%}$

Notice that we needed to add zeros at the end of the number when moving the decimal two places to the right.

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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.

When we first looked at fractions and decimals, we saw that fractions converted to a repeating decimal    . When we converted the fraction $\frac{4}{3}$ to a decimal, we wrote the answer as $1.\overline{3}.$ We will use this same notation, as well as fraction notation, when we convert fractions to percents in the next example.

An article in a medical journal claimed that approximately $\frac{1}{3}$ of American adults are obese. Convert the fraction $\frac{1}{3}$ to a percent.

Solution

	$\frac{1}{3}$
Change to a decimal.
Write as a repeating decimal.	$0.333\dots$
Write as a percent.	$33\frac{1}{3}\%$

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We could also write the percent as $33.3\%$ .

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Key concepts

• A percent is a ratio whose denominator is $100.$ See [link] .
• Percents can be converted to fractions and decimals. To convert a percent to a fraction, write it as a ratio with the denominator $100.$ To convert to a decimal, then divide the numerator by the denominator. See [link] .
• A decimal can be converted to a percent by moving the decimal point two places to the right and adding a percent sign. A fraction can be converted to a percent by first converting it to a decimal. See [link] .