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We can convert a decimal fraction to a fraction, essentially, by saying it in words, then writing what we say. We may have to reduce that fraction.
Convert each decimal fraction to a proper fraction or a mixed number.
Reading: six tenths→ $\frac{6}{10}$ .
Reduce: $\frac{3}{5}$ .
Reading: nine hundred three thousands→ $\frac{\text{903}}{\text{1000}}$ .
Reading: eighteen and sixty-one hundredths→ $\text{18}\frac{\text{61}}{\text{100}}$ .
Reading: five hundred eight and five ten thousandths→ $\text{508}\frac{5}{\text{10},\text{000}}$ .
Reduce: $\text{508}\frac{1}{\mathrm{2,}\text{000}}$ .
Convert the following decimals to fractions or mixed numbers. Be sure to reduce.
6,646.0107
$\mathrm{6,}\text{646}\frac{\text{107}}{\text{10},\text{000}}$
Convert the following complex decimals to fractions.
$0\text{.}\text{11}\frac{2}{3}$
The $\frac{2}{3}$ appears to occur in the thousands position, but it is referring to $\frac{2}{3}$ of a hundredth. So, we read $0\text{.}\text{11}\frac{2}{3}$ as "eleven and two-thirds hundredths."
$\begin{array}{ccc}0.11\frac{2}{3}=\frac{\text{11}\frac{2}{3}}{\text{100}}& =& \frac{\frac{\text{11}\cdot 3+2}{3}}{\text{100}}\\ & =& \frac{\frac{\text{35}}{3}}{\frac{\text{100}}{1}}\hfill \\ & =& \frac{\text{35}}{3}\xf7\frac{\text{100}}{1}\hfill \\ & =& \frac{\stackrel{7}{\overline{)35}}}{3}\cdot \frac{1}{\underset{\text{20}}{\overline{)100}}}\hfill \\ & =& \frac{7}{\text{60}}\hfill \end{array}$
$4\text{.}\text{006}\frac{1}{4}$
Note that $4\text{.}\text{006}\frac{1}{4}=4+\text{.}\text{006}\frac{1}{4}$
$\begin{array}{ccc}\hfill 4+.006\frac{1}{4}& =& 4+\frac{6\frac{1}{4}}{\text{1000}}\hfill \\ & =& 4+\frac{\frac{\text{25}}{4}}{\frac{\text{1000}}{1}}\hfill \\ & =& 4+\frac{\stackrel{1}{\overline{)25}}}{4}\cdot \frac{1}{\underset{40}{\overline{)1000}}}\hfill \\ & =& 4+\frac{1\cdot 1}{4\cdot \text{40}}\hfill \\ & =& 4+\frac{1}{\text{160}}\hfill \\ & =& 4\frac{1}{\text{160}}\hfill \end{array}$
Convert each complex decimal to a fraction or mixed number. Be sure to reduce.
$0\text{.}\text{12}\frac{2}{5}$
$\frac{\text{31}}{\text{250}}$
$6\text{.}\text{005}\frac{5}{6}$
$6\frac{7}{\mathrm{1,}\text{200}}$
$\text{18}\text{.}1\frac{3}{\text{17}}$
$\text{18}\frac{2}{\text{17}}$
For the following 20 problems, convert each decimal fraction to a proper fraction or a mixed number. Be sure to reduce.
9.99995
$9\frac{\text{19},\text{999}}{\text{20},\text{000}}$
For the following 10 problems, convert each complex decimal to a fraction.
$0\text{.}\text{012}\frac{1}{2}$
$2\text{.}\text{16}\frac{1}{4}$
$2\frac{\text{13}}{\text{80}}$
$5\text{.}\text{18}\frac{2}{3}$
$\text{14}\text{.}\text{112}\frac{1}{3}$
$\text{14}\frac{\text{337}}{\mathrm{3,}\text{000}}$
$\text{80}\text{.}\text{0011}\frac{3}{7}$
$1\text{.}\text{40}\frac{5}{\text{16}}$
$1\frac{\text{129}}{\text{320}}$
$0\text{.}8\frac{5}{3}$
$1\text{.}7\frac{\text{37}}{9}$
( [link] ) Find the greatest common factor of 70, 182, and 154.
14
( [link] ) Find the greatest common multiple of 14, 26, and 60.
( [link] ) Find the value of $\frac{3}{5}\cdot \frac{\text{15}}{\text{18}}\xf7\frac{5}{9}$ .
$\frac{9}{\text{10}}$
( [link] ) Find the value of $5\frac{2}{3}+8\frac{1}{\text{12}}$ .
( [link] ) In the decimal number 26.10742, the digit 7 is in what position?
thousandths
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