8.6 Decimals: converting a fraction to a decimal

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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to convert a fraction to a decimal. By the end of the module students should 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, $\frac{3}{4}$ not only means "3 objects out of 4," but can also mean "3 divided by 4."

Sample set a

Convert the following fractions to decimals. If the division is nonterminating, round to two decimal places.

$\frac{3}{4}$ . Divide 3 by 4.

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.

$\frac{1}{8}=\text{.}\text{125}$

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.

Thus, $0\text{.}\text{16}\frac{1}{4}=0\text{.}\text{1625}$ .

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.

$\frac{1}{4}$

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

Exercises

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

$\frac{\text{10}}{\text{11}}$

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.

$\frac{\text{16}}{\text{125}}$

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

Exercises for review

( [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. $\text{30}÷1\text{.}1$ .

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