2.8: Percents
- Page ID
- 176513
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Convert Decimals, Fractions, and Percents
In our work, it is often necessary to change the form of a number. We may have to change fractions to decimals or decimals to percent.
We convert decimals into fractions by identifying the place value of the last (farthest right) digit. In the decimal 0.03. the 3 is in the hundredths place, so 100 is the denominator of the fraction equivalent to 0.03.
\[0.03=\dfrac{3}{100}\]
The steps to take to convert a decimal to a fraction are summarized in the procedure box.
- To convert a decimal to a proper fraction, determine the place value of the final digit.
- Write the fraction.
- numerator—the “numbers” to the right of the decimal point
- denominator—the place value corresponding to the final digit
- To convert a fraction to a decimal, divide the numerator of the fraction by the denominator of the fraction.
Write: ⓐ \(0.374\) as a fraction ⓑ \(−\frac{5}{8}\) as a decimal.
- Answer
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ⓐ
Determine the place value of the final digit. 
Write the fraction for 0.374: The numerator is 374. The denominator is 1,000. 
Simplify the fraction. 
Divide out the common factors. 
ⓑ Since a fraction bar means division, we begin by writing the fraction \(\frac{5}{8}\) as \(8\sqrt{5}\). Now divide.
Write: ⓐ \(0.234\) as a fraction ⓑ \(−\frac{7}{8}\) as a decimal.
- Answer
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ⓐ\(\frac{117}{500}\) ⓑ \(−0.875\)
Write: ⓐ \(0.024\) as a fraction ⓑ \(−\frac{3}{8}\) as a decimal.
- Answer
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ⓐ\(\frac{3}{125}\) ⓑ \(−0.375\)
A percent is a ratio whose denominator is 100. Percent means per hundred. We use the percent symbol, %, to show percent. Since a percent is a ratio, it can easily be expressed as a fraction. Percent means per 100, so the denominator of the fraction is 100. We then change the fraction to a decimal by dividing the numerator by the denominator. After doing this many times, you may see the pattern.
To convert a percent number to a decimal number, we move the decimal point two places to the left.
To convert a decimal to a percent, remember that percent means per hundred. If we change the decimal to a fraction whose denominator is 100, it is easy to change that fraction to a percent. After many conversions, you may recognize the pattern.
To convert a decimal to a percent, we move the decimal point two places to the right and then add the percent sign.
- To convert a percent to a decimal, move the decimal point two places to the left after removing the percent sign.
- To convert a decimal to a percent, move the decimal point two places to the right and then add the percent sign.
Convert each:
ⓐ percent to a decimal: 62%, 135%, and 13.7%.
ⓑ decimal to a percent: 0.51, 1.25, and 0.093.
- Answer
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ⓐ
Move the decimal point two places to the left. 
ⓑ
Move the decimal point two places to the right. 
Convert each:
ⓐ percent to a decimal: 9%, 87%, and 3.9%.
ⓑ decimal to a percent: 0.17, 1.75, and 0.0825.
- Answer
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ⓐ 0.09, 0.87, 0.039 ⓑ 17%, 175%, 8.25%
Convert each:
ⓐ percent to a decimal: 3%, 91%, and 8.3%.
ⓑ decimal to a percent: 0.41, 2.25, and 0.0925.
- Answer
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ⓐ 0.03, 0.91, 0.083 ⓑ 41%, 225%, 9.25%