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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, $\frac{3}{4}$ 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.
$\frac{3}{4}$ . Divide 3 by 4.
$\begin{array}{c}\hfill .75\\ \hfill 4\overline{)3.00}\\ \hfill \underline{28}\\ \hfill 20\\ \hfill \underline{20}\\ \hfill 0\end{array}$
Thus, $\frac{3}{4}=0\text{.}\text{75}$ .
$\frac{1}{5}$ Divide 1 by 5.
$\begin{array}{c}\hfill .2\\ \hfill 5\overline{)1.0}\\ \hfill \underline{1.0}\\ \hfill 0\end{array}$
Thus, $\frac{1}{5}=0\text{.}2$
$\frac{5}{6}$ . Divide 5 by 6.
$\frac{5}{6}=0\text{.}\text{833}\cdots $ We are to round to two decimal places.
Thus, $\frac{5}{6}=0\text{.}\text{83}$ to two decimal places.
$5\frac{1}{8}$ . Note that $5\frac{1}{8}=5+\frac{1}{8}$ .
Convert $\frac{1}{8}$ to a decimal.
$\begin{array}{c}\hfill .125\\ \hfill 8\overline{)1.000}\\ \hfill \underline{8}\\ \hfill 20\\ \hfill \underline{16}\\ \hfill 40\\ \hfill \underline{40}\\ \hfill 0\end{array}$
$\frac{1}{8}=\text{.}\text{125}$
Thus, $5\frac{1}{8}=5+\frac{1}{8}=5+\text{.}\text{125}=5\text{.}\text{125}$ .
$0\text{.}\text{16}\frac{1}{4}$ . This is a complex decimal.
Note that the 6 is in the hundredths position.
The number $0\text{.}\text{16}\frac{1}{4}$ is read as "sixteen and one-fourth hundredths."
$0\text{.}\text{16}\frac{1}{4}=\frac{\text{16}\frac{1}{4}}{\text{100}}=\frac{\frac{\text{16}\cdot 4+1}{4}}{\text{100}}=\frac{\frac{\text{65}}{4}}{\frac{\text{100}}{1}}=\frac{\stackrel{\text{13}}{\overline{)\text{65}}}}{4}\cdot \frac{1}{\underset{\text{20}}{\overline{)\text{100}}}}=\frac{\text{13}\cdot 1}{4\cdot \text{20}}=\frac{\text{13}}{\text{80}}$
Now, convert $\frac{\text{13}}{\text{80}}$ to a decimal.
$\begin{array}{c}\hfill .1625\\ \hfill 80\overline{)13.0000}\\ \hfill \underline{80}\\ \hfill 500\\ \hfill \underline{480}\\ \hfill 200\\ \hfill \underline{160}\\ \hfill 400\\ \hfill \underline{400}\\ \hfill 0\end{array}$
Thus, $0\text{.}\text{16}\frac{1}{4}=0\text{.}\text{1625}$ .
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.
$\frac{1}{4}$
0.25
$\frac{1}{\text{25}}$
0.04
$\frac{1}{6}$
0.17
$\frac{\text{15}}{\text{16}}$
0.9375
$0\text{.}9\frac{1}{2}$
0.95
$8\text{.}\text{0126}\frac{3}{8}$
8.0126375
For the following 30 problems, convert each fraction or complex decimal number to a decimal (in which no proper fractions appear).
$\frac{1}{2}$
0.5
$\frac{4}{5}$
$\frac{7}{8}$
0.875
$\frac{5}{8}$
$\frac{3}{5}$
0.6
$\frac{2}{5}$
$\frac{1}{\text{25}}$
0.04
$\frac{3}{\text{25}}$
$\frac{1}{\text{20}}$
0.05
$\frac{1}{\text{15}}$
$\frac{1}{\text{50}}$
0.02
$\frac{1}{\text{75}}$
$\frac{1}{3}$
$0\text{.}\overline{3}$
$\frac{5}{6}$
$\frac{3}{\text{16}}$
0.1875
$\frac{9}{\text{16}}$
$\frac{1}{\text{27}}$
$0\text{.}0\overline{\text{37}}$
$\frac{5}{\text{27}}$
$\frac{7}{\text{13}}$
$0\text{.}\overline{\text{538461}}$
$\frac{9}{\text{14}}$
$7\frac{2}{3}$
$7\text{.}\overline{6}$
$8\frac{5}{\text{16}}$
$1\frac{2}{\text{15}}$
$1\text{.}1\overline{3}$
$\text{65}\frac{5}{\text{22}}$
$\text{101}\frac{6}{\text{25}}$
101.24
$0\text{.}1\frac{1}{2}$
$0\text{.}\text{24}\frac{1}{8}$
0.24125
$5\text{.}\text{66}\frac{2}{3}$
$\text{810}\text{.}\text{3106}\frac{5}{\text{16}}$
810.31063125
$4\text{.}1\frac{1}{9}$
For the following 18 problems, convert each fraction to a decimal. Round to five decimal places.
$\frac{1}{9}$
0.11111
$\frac{2}{9}$
$\frac{3}{9}$
0.33333
$\frac{4}{9}$
$\frac{5}{9}$
0.55556
$\frac{6}{9}$
$\frac{7}{9}$
0.77778
$\frac{8}{9}$
$\frac{1}{\text{11}}$
0.09091
$\frac{2}{\text{11}}$
$\frac{3}{\text{11}}$
0.27273
$\frac{4}{\text{11}}$
$\frac{5}{\text{11}}$
0.45455
$\frac{6}{\text{11}}$
$\frac{7}{\text{11}}$
0.63636
$\frac{8}{\text{11}}$
$\frac{9}{\text{11}}$
0.81818
$\frac{\text{10}}{\text{11}}$
$\frac{\text{16}}{\text{125}}$
0.128
$\frac{\text{85}}{\text{311}}$
$\frac{\text{192}}{\text{197}}$
0.9746
$\frac{1}{\text{1469}}$
$\frac{4}{\text{21},\text{015}}$
0.0002
$\frac{\text{81},\text{426}}{\text{106},\text{001}}$
$\frac{\text{16},\text{501}}{\text{426}}$
38.7347
( [link] ) Round 2,105,106 to the nearest hundred thousand.
( [link] ) $\frac{8}{5}$ of what number is $\frac{3}{2}$ ?
$\frac{\text{15}}{\text{16}}$
( [link] ) Arrange $1\frac{9}{\text{16}}$ , $1\frac{5}{8}$ , and $1\frac{7}{\text{12}}$ in increasing order.
( [link] ) Convert the complex decimal $3\text{.}6\frac{5}{4}$ to a fraction.
$3\frac{\text{29}}{\text{40}}$ or 3.725
( [link] ) Find the quotient. $\text{30}\xf71\text{.}1$ .
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