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Percents such as $\frac{1}{2}$ %, $\frac{3}{5}$ %, $\frac{5}{8}$ %, and $\frac{7}{\text{11}}$ %, where 1% has not been attained, are fractions of 1%. This implies that
$\frac{1}{2}\%\text{}=\frac{1}{2}\text{of 1\%}$
$\frac{3}{5}\%\text{}=\frac{3}{5}\text{of 1\%}$
$\frac{5}{8}\%\text{}=\frac{5}{8}\text{of 1\%}$
$\frac{7}{\text{11}}\%\text{}=\frac{7}{\text{11}}\text{of 1\%}$
Since "percent" means "for each hundred," and "of" means "times," we have
$\frac{1}{2}\%\text{}=\frac{1}{2}\text{of 1\%}=\frac{1}{2}\cdot \frac{1}{\text{100}}=\frac{1}{\text{200}}$
$\frac{3}{5}\%\text{}=\frac{3}{5}\text{of 1\%}=\frac{3}{5}\cdot \frac{1}{\text{100}}=\frac{3}{\text{500}}$
$\frac{5}{8}\%\text{}=\frac{5}{8}\text{of 1\%}=\frac{5}{8}\cdot \frac{1}{\text{100}}=\frac{5}{\text{800}}$
$\frac{7}{\text{11}}\%\text{}=\frac{7}{\text{11}}\text{of 1\%}=\frac{7}{\text{11}}\cdot \frac{1}{\text{100}}=\frac{7}{\text{1100}}$
Convert $\frac{2}{3}$ % to a fraction.
$\begin{array}{ccc}\hfill \frac{2}{3}\%=\frac{2}{3}\phantom{\rule{2px}{0ex}}\text{of}\phantom{\rule{2px}{0ex}}1\%& =& \frac{\stackrel{1}{\overline{)2}}}{3}\cdot \frac{1}{\underset{50}{\overline{)100}}}\hfill \\ & =& \frac{1\cdot 1}{3\cdot 50}\hfill \\ & =& \frac{1}{150}\hfill \end{array}$
Convert $\frac{5}{8}$ % to a decimal.
$\begin{array}{ccc}\hfill \frac{5}{8}\%=\frac{5}{8}\phantom{\rule{2px}{0ex}}\text{of}\phantom{\rule{2px}{0ex}}1\%& =& \frac{5}{8}\cdot \frac{1}{100}\hfill \\ & =& 0.625\cdot 0.01\hfill \\ & =& 0.00625\hfill \end{array}$
Convert $\frac{1}{4}$ % to a fraction.
$\frac{1}{\text{400}}$
Convert $\frac{3}{8}$ % to a fraction.
$\frac{3}{\text{800}}$
Convert $3\frac{1}{3}$ % to a fraction.
$\frac{1}{\text{30}}$
We must be careful when changing a fraction of 1% to a decimal. The number $\frac{2}{3}$ , as we know, has a nonterminating decimal representation. Therefore, it cannot be expressed exactly as a decimal.
When converting nonterminating fractions of 1% to decimals, it is customary to express the fraction as a rounded decimal with at least three decimal places.
Convert $\frac{2}{3}$ % to a three-place decimal.
Since we wish the resulting decimal to have three decimal digits, and removing the percent sign will account for two of them, we need to round $\frac{2}{3}$ to one place $(\text{2}+\text{1}=\text{3})$ .
$\frac{2}{3}\%\text{}=0\text{.}7\text{}$ % to one decimal place. $\left(\frac{2}{3}=0\text{.}\text{6666}\dots \right)$
$\frac{2}{3}\text{\%}=\text{0}\text{.}\text{007}$ to 3 decimal places
Convert $5\frac{4}{\text{11}}$ % to a four-place decimal.
$5\frac{4}{\text{11}}\%\text{}=5\text{.}\text{36}\text{}\%$ to two decimal places. $\left(\frac{4}{\text{11}}=0\text{.}\text{3636}\dots \right)$
$5\frac{4}{\text{11}}\%\text{}=0\text{.}\text{0536}\text{}$ to four decimal places.
Convert $\text{28}\frac{5}{9}$ % to a decimal rounded to ten thousandths.
$\text{28}\frac{5}{9}\%\text{}=\text{28}\text{.}\text{56\%}\text{}$ to two decimal places. $\left(\frac{5}{9}=0\text{.}\text{5555}\dots \right)$
$\text{28}\frac{5}{9}\%\text{}=0\text{.}\text{2856}$ correct to ten thousandths.
Convert $\text{51}\frac{5}{11}\%$ to a decimal rounded to ten thousandths.
0.5145
Make the conversions as indicated.
Convert $\frac{3}{4}$ % to a fraction.
$\frac{3}{\text{400}}$
Convert $\frac{5}{6}$ % to a fraction.
Convert $\frac{1}{9}$ % to a fraction.
$\frac{1}{\text{900}}$
Convert $\frac{\text{15}}{\text{19}}$ % to a fraction.
Convert $\frac{5}{4}$ % to a fraction.
$\frac{5}{\text{400}}\text{or}\frac{1}{\text{80}}$
Convert $\frac{7}{3}$ % to a fraction.
Convert $1\frac{6}{7}$ % to a fraction.
$\frac{\text{13}}{\text{700}}$
Convert $2\frac{5}{\text{16}}$ % to a fraction.
Convert $\text{25}\frac{1}{4}$ % to a fraction.
$\frac{\text{101}}{\text{400}}$
Convert $\text{50}\frac{1}{2}$ % to a fraction.
Convert $\text{72}\frac{3}{5}$ % to a fraction.
$\frac{\text{363}}{\text{500}}$
Convert $\text{99}\frac{1}{8}$ % to a fraction.
Convert $\text{136}\frac{2}{3}$ % to a fraction.
$\frac{\text{41}}{\text{30}}$
Convert $\text{521}\frac{3}{4}$ % to a fraction.
Convert $\text{10}\frac{1}{5}$ % to a decimal.
$\frac{\text{51}}{\text{500}}=0\text{.}\text{102}$
Convert $\text{12}\frac{3}{4}$ % to a decimal.
Convert $3\frac{7}{8}$ % to a decimal.
$\frac{\text{31}}{\text{800}}=0\text{.}\text{03875}$
Convert $7\frac{1}{\text{16}}$ % to a decimal.
Convert $\frac{3}{7}$ % to a three-place decimal.
$0\text{.}\text{004}$
Convert $\frac{1}{9}$ % to a three-place decimal.
Convert $6\frac{3}{\text{11}}$ % to a four-place decimal.
0.0627
Convert $9\frac{2}{7}$ % to a four-place decimal.
Convert $\text{24}\frac{5}{\text{21}}$ % to a three-place decimal.
0.242
Convert $\text{45}\frac{8}{\text{27}}$ % to a three-place decimal.
Convert $\text{11}\frac{\text{16}}{\text{17}}$ % to a four-place decimal.
0.1194
Convert $5\frac{1}{7}$ % to a three-place decimal.
( [link] ) Write $\text{8}\cdot \text{8}\cdot \text{8}\cdot \text{8}\cdot \text{8}$ using exponents.
${8}^{5}$
( [link] ) Convert $4\frac{7}{8}$ to an improper fraction.
( [link] ) Find the sum. $\frac{7}{\text{10}}+\frac{2}{\text{21}}+\frac{1}{7}$ .
$\frac{\text{197}}{\text{210}}$
( [link] ) Find the product. $(4\text{.}\text{21})(0\text{.}\text{006})$ .
( [link] ) Convert 8.062 to a percent.
$\text{806}\text{.}2\text{}$ %
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