6.8: Converting a Fraction to a Decimal
- Page ID
- 52602
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- be able to convert a fraction to a decimal
Now that we have studied and practiced dividing with decimals, we are also able to convert a fraction to a decimal. To do so we need only recall that a fraction bar can also be a division symbol. Thus, \(\dfrac{3}{4}\) not only means "3 objects out of 4," but can also mean "3 divided by 4."
Convert the following fractions to decimals. If the division is nonterminating, round to two decimal places.
\(\dfrac{3}{4}\). Divide 3 by 4.
Solution
\(\begin{array} {.75} \\ {4\overline{)3.00}} \\ {\underline{2.8\ \ }} \\ {20} \\ {\underline{20}} \\ {0} \end{array}\)
Thus, \(\dfrac{3}{4} = 0.75\).
\(\dfrac{1}{5}\). Divide 1 by 5.
Solution
\(\begin{array} {.2} \\ {5\overline{)1.0}} \\ {\underline{1.0}} \\ {0} \end{array}\)
Thus, \(\dfrac{1}{5} = 0.2\).
\(\dfrac{5}{6}\). Divide 5 by 6.
Solution
\(\dfrac{5}{6} = 0.833...\) We are to round to two decimal places.
Thus, \(\dfrac{5}{6} = 0.83\) to two decimal places.
\(5 \dfrac{1}{8}\). Note that \(5 \dfrac{1}{8} = 5 + \dfrac{1}{8}\)
Solution
Convert \(\dfrac{1}{8}\) to a decimal.
\(\begin{array} {r} {.125} \\ {8\overline{)1.000}} \\ {\underline{\ \ \ 8\ \ \ \ }} \\ {20\ \ } \\ {\underline{16\ \ }} \\ {40} \\ {\underline{40}} \\ {0} \end{array}\)
\(\dfrac{1}{8} = .125\)
Thus, \(5 \dfrac{1}{8} = 5 + \dfrac{1}{8} = 5 + .125 = 5.125\).
\(0.16 \dfrac{1}[4}\). This is a complex decimal.
Solution
Note that the 6 is in the hundredths position.
The number \(0.16\dfrac{1}{4}\) is read as "sixteen and one-fourth hundredths."
\(0.16 \dfrac{1}{4} = \dfrac{16\dfrac{1}{4}}{100} = \dfrac{\dfrac{16 \cdot 4 + 1}{4}}{100} = \dfrac{\dfrac{65}{4}}{\dfrac{100}{1}} = \dfrac{\begin{array} {c} {^{13}} \\ {\cancel{65}} \end{array}}{4} \cdot \dfrac{1}{\begin{array} {c} {\cancel{100}} \\ {^{20}} \end{array}} = \dfrac{13 \cdot 1}{4 \cdot 20} = \dfrac{13}{80}.\)
Now, convert \(\dfrac{13}{80}\) to a decimal.
\(\begin{array} {r} {.1625} \\ {80\overline{)13.0000}} \\ {\underline{8\ 0\ \ \ \ \ \ }} \\ {5\ 00\ \ \ \ } \\ {\underline{4\ 80\ \ \ \ }} \\ {200\ \ } \\ {\underline{160\ \ }} \\ {400} \\ {\underline{400}} \\ {0} \end{array}\)
Thus, \(0.16 \dfrac{1}{4} = 0.1625\).
Practice Set A
Convert the following fractions and complex decimals to decimals (in which no proper fractions appear). If the divison is nonterminating, round to two decimal places.
\(\dfrac{1}{4}\)
- Answer
-
0.25
Practice Set A
\(\dfrac{1}{25}\)
- Answer
-
0.04
Practice Set A
\(\dfrac{1}{6}\)
- Answer
-
0.17
Practice Set A
\(\dfrac{15}{16}\)
- Answer
-
0.9375
Practice Set A
\(0.9 \dfrac{1}{2}\)
- Answer
-
0.95
Practice Set A
\(8.0126 \dfrac{3}{8}\)
- Answer
-
8.0126375
Exercises
For the following 30 problems, convert each fraction or complex decimal number to a decimal (in which no proper fractions appear).
Exercise \(\PageIndex{1}\)
\(\dfrac{1}{2}\)
- Answer
-
0.5
Exercise \(\PageIndex{2}\)
\(\dfrac{4}{5}\)
Exercise \(\PageIndex{3}\)
\(\dfrac{7}{8}\)
- Answer
-
0.875
Exercise \(\PageIndex{4}\)
\(\dfrac{5}{8}\)
Exercise \(\PageIndex{5}\)
\(\dfrac{3}{5}\)
- Answer
-
0.6
Exercise \(\PageIndex{6}\)
\(\dfrac{2}{5}\)
Exercise \(\PageIndex{7}\)
\(\dfrac{1}{25}\)
- Answer
-
0.04
Exercise \(\PageIndex{8}\)
\(\dfrac{3}{25}\)
Exercise \(\PageIndex{9}\)
\(\dfrac{1}{20}\)
- Answer
-
0.05
Exercise \(\PageIndex{10}\)
\(\dfrac{1}{15}\)
Exercise \(\PageIndex{11}\)
\(\dfrac{1}{50}\)
- Answer
-
0.02
Exercise \(\PageIndex{12}\)
\(\dfrac{1}{75}\)
Exercise \(\PageIndex{13}\)
\(\dfrac{1}{3}\)
- Answer
-
\(0.\overline{3}\)
Exercise \(\PageIndex{14}\)
\(\dfrac{5}{6}\)
Exercise \(\PageIndex{15}\)
\(\dfrac{3}{16}\)
- Answer
-
0.1875
Exercise \(\PageIndex{16}\)
\(\dfrac{9}{16}\)
Exercise \(\PageIndex{17}\)
\(\dfrac{1}{27}\)
- Answer
-
\(0.0\overline{37}\)
Exercise \(\PageIndex{18}\)
\(\dfrac{5}{27}\)
Exercise \(\PageIndex{19}\)
\(\dfrac{7}{13}\)
- Answer
-
\(0.\overline{538461}\)
Exercise \(\PageIndex{20}\)
\(\dfrac{9}{14}\)
Exercise \(\PageIndex{21}\)
\(7 \dfrac{2}{3}\)
- Answer
-
\(7.\overline{6}\)
Exercise \(\PageIndex{22}\)
\(8\dfrac{5}{16}\)
Exercise \(\PageIndex{23}\)
\(1 \dfrac{2}{15}\)
- Answer
-
\(1.1\overline{3}\)
Exercise \(\PageIndex{24}\)
\(65\dfrac{5}{22}\)
Exercise \(\PageIndex{25}\)
\(101 \dfrac{6}{25}\)
- Answer
-
101.24
Exercise \(\PageIndex{26}\)
\(0.1 \dfrac{1}{2}\)
Exercise \(\PageIndex{27}\)
\(0.24\dfrac{1}{8}\)
- Answer
-
0.24125
Exercise \(\PageIndex{28}\)
\(5.66 \dfrac{2}{3}\)
Exercise \(\PageIndex{29}\)
\(810.3106 \dfrac{5}{16}\)
- Answer
-
810.31063125
Exercise \(\PageIndex{30}\)
\(4.1 \dfrac{1}{9}\)
For the following 18 problems, convert each fraction to a decimal. Round to five decimal places.
Exercise \(\PageIndex{31}\)
\(\dfrac{1}{9}\)
- Answer
-
0.11111
Exercise \(\PageIndex{32}\)
\(\dfrac{2}{9}\)
Exercise \(\PageIndex{33}\)
\(\dfrac{3}{9}\)
- Answer
-
0.33333
Exercise \(\PageIndex{34}\)
\(\dfrac{4}{9}\)
Exercise \(\PageIndex{35}\)
\(\dfrac{5}{9}\)
- Answer
-
0.55556
Exercise \(\PageIndex{36}\)
\(\dfrac{6}{9}\)
Exercise \(\PageIndex{37}\)
\(\dfrac{7}{9}\)
- Answer
-
0.77778
Exercise \(\PageIndex{38}\)
\(\dfrac{8}{9}\)
Exercise \(\PageIndex{39}\)
\(\dfrac{1}{11}\)
- Answer
-
0.09091
Exercise \(\PageIndex{40}\)
\(\dfrac{2}{11}\)
Exercise \(\PageIndex{41}\)
\(\dfrac{3}{11}\)
- Answer
-
0.27273
Exercise \(\PageIndex{42}\)
\(\dfrac{4}{11}\)
Exercise \(\PageIndex{43}\)
\(\dfrac{5}{11}\)
- Answer
-
0.45455
Exercise \(\PageIndex{44}\)
\(\dfrac{6}{11}\)
Exercise \(\PageIndex{45}\)
\(\dfrac{7}{11}\)
- Answer
-
0.63636
Exercise \(\PageIndex{46}\)
\(\dfrac{8}{11}\)
Exercise \(\PageIndex{47}\)
\(\dfrac{9}{11}\)
- Answer
-
0.81818
Exercise \(\PageIndex{48}\)
\(\dfrac{10}{11}\)
Calculator Problems
For the following problems, use a calculator to convert each fraction to a decimal. If no repeating pattern seems to exist, round to four decimal places.
Exercise \(\PageIndex{49}\)
\(\dfrac{16}{125}\)
- Answer
-
0.128
Exercise \(\PageIndex{50}\)
\(\dfrac{85}{311}\)
Exercise \(\PageIndex{51}\)
\(\dfrac{192}{197}\)
- Answer
-
0.9746
Exercise \(\PageIndex{52}\)
\(\dfrac{1}{1469}\)
Exercise \(\PageIndex{53}\)
\(\dfrac{4}{21,015}\)
- Answer
-
0.0002
Exercise \(\PageIndex{54}\)
\(\dfrac{81,426}{106,001}\)
Exercise \(\PageIndex{55}\)
\(\dfrac{16,501}{426}\)
- Answer
-
38.7347
Exercises for Review
Exercise \(\PageIndex{56}\)
Round 2,105,106 to the nearest hundred thousand.
Exercise \(\PageIndex{57}\)
\(\dfrac{8}{5}\) of what number is \(\dfrac{3}{2}\)?
- Answer
-
\(\dfrac{15}{16}\)
Exercise \(\PageIndex{58}\)
Arrange \(1 \dfrac{9}{16}\), \(1 \dfrac{5}{8}\), and \(1 \dfrac{7}{12}\) in increasing order.
Exercise \(\PageIndex{59}\)
Convert the complex decimal \(3.6 \dfrac{5}{4}\) to a fraction.
- Answer
-
\(3 \dfrac{29}{40}\) or 3.725
Exercise \(\PageIndex{60}\)
Find the quotient. \(30 \div 1.1\).