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The word percent comes from the Latin word “per centum,” “per” meaning “for each,” and “centum” meaning “hundred.”
Thus, $\begin{array}{rrrrr}\hfill 1\%=\frac{1}{100}& \hfill & \hfill \text{or}& \hfill & \hfill 1\%=\mathrm{0.01.}\end{array}$
We can see how a fraction can be converted to a percent by analyzing the method that $\frac{3}{5}$ is converted to a percent. In order to convert $\frac{3}{5}$ to a percent, we need to introduce $\frac{1}{100}$ (since percent means for each hundred).
$$\begin{array}{rrrrr}\hfill \frac{3}{5}& \hfill =& \frac{3}{5}\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{100}{100}\hfill & \hfill & \text{Multiply\hspace{0.17em}the\hspace{0.17em}fraction\hspace{0.17em}by\hspace{0.17em}1}.\hfill \\ \hfill & \hfill =& \frac{3}{5}\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}100\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill & \hfill & \text{Since \hspace{0.17em}}\frac{100}{100}=100\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}.\hfill \\ \hfill & \hfill =& \frac{300}{5}\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill & \hfill & \text{Divide\hspace{0.17em}}300\text{\hspace{0.17em}by\hspace{0.17em}5}.\hfill \\ \hfill & \hfill =& 60\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill & \hfill & \text{Multiply\hspace{0.17em}the\hspace{0.17em}fractions}.\hfill \\ \hfill & \hfill =& 60\%\hfill & \hfill & \text{Replace\hspace{0.17em}}\frac{1}{100}\text{\hspace{0.17em}}\text{with\hspace{0.17em}the\hspace{0.17em}}\%\text{\hspace{0.17em}symbol}.\hfill \end{array}$$
Convert each fraction to a percent.
$$\begin{array}{lll}\frac{1}{4}\hfill & =\hfill & \frac{1}{4}\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}100\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & \frac{100}{4}\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & 25\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & 25\%\hfill \end{array}$$
$$\begin{array}{lll}\frac{8}{5}\hfill & =\hfill & \frac{8}{5}\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}100\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & \frac{800}{5}\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & 160\%\hfill \end{array}$$
$$\begin{array}{lll}\frac{4}{9}\hfill & =\hfill & \frac{4}{9}\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}100\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & \frac{400}{9}\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & \left(\mathrm{44.4...}\right)\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & \left(44.\overline{4}\right)\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & 44.\overline{4}\%\hfill \end{array}$$
We can see how a decimal is converted to a percent by analyzing the method that
$0.75$ is converted to a percent. We need to introduce
$\frac{1}{100}.$
$$\begin{array}{lllll}0.75\hfill & =\hfill & 0.75\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}100\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill & \hfill & \text{Multiply\hspace{0.17em}the\hspace{0.17em}decimal\hspace{0.17em}by\hspace{0.17em}1}\text{.}\hfill \\ \hfill & =\hfill & 75\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill & \hfill & \hfill \\ \hfill & =\hfill & 75\%\hfill & \hfill & \text{Replace\hspace{0.17em}}\frac{1}{100}\text{\hspace{0.17em}with\hspace{0.17em}the\hspace{0.17em}\%\hspace{0.17em}symbol}.\hfill \end{array}$$
Convert each decimal to a percent.
$$\begin{array}{lll}0.62\hfill & =\hfill & 0.62\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}100\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & 62\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & 62\%\hfill \end{array}$$
Notice that the decimal point in the original number has been moved to the right 2 places.
$$\begin{array}{lll}8.4\hfill & =\hfill & 8.4\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}100\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & 840\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & 840\%\hfill \end{array}$$
Notice that the decimal point in the original number has been moved to the right 2 places.
$$\begin{array}{lll}0.47623\hfill & =\hfill & 0.47623\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}100\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & 0.47623\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & 47.623\%\hfill \end{array}$$
Notice that the decimal point in the original number has been moved to the right 2 places.
We can see how a percent is converted to a decimal by analyzing the method that 12% is converted to a decimal. We need to introduce
$\frac{1}{100}.$
$$\begin{array}{lllll}12\%\hfill & =\hfill & 12\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill & \hfill & \text{Replace}\text{\hspace{0.17em}}\%\text{\hspace{0.17em}}\text{with}\text{\hspace{0.17em}}\frac{1}{100}.\hfill \\ \hfill & =\hfill & \frac{12}{100}\hfill & \hfill & \text{Multiply\hspace{0.17em}the\hspace{0.17em}fractions}.\hfill \\ \hfill & =\hfill & 0.12\hfill & \hfill & \text{Divide\hspace{0.17em}12\hspace{0.17em}by\hspace{0.17em}1}00.\hfill \end{array}$$
Convert each percent to a decimal.
$$\begin{array}{lll}48\%\hfill & =\hfill & 48\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & \frac{48}{100}\hfill \\ \hfill & =\hfill & 0.48\hfill \end{array}$$
Notice that the decimal point in the original number has been moved to the left 2 places.
$$\begin{array}{lll}659\%\hfill & =\hfill & 659\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & \frac{659}{100}\hfill \\ \hfill & =\hfill & 6.59\hfill \end{array}$$
Notice that the decimal point in the original number has been moved to the left 2 places.
$$\begin{array}{lll}0.4113\%\hfill & =\hfill & 0.4113\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{1}{100}\hfill \\ \hfill & =\hfill & \frac{0.4113}{100}\hfill \\ \hfill & =\hfill & 0.004113\hfill \end{array}$$
Notice that the decimal point in the original number has been moved to the left 2 places.
For the following problems, convert each fraction to a percent.
$\frac{7}{8}$
$\frac{5}{16}$
$\frac{2}{11}$
$\frac{16}{45}$
$\frac{7}{27}$
For the following problems, convert each decimal to a percent.
For the following problems, convert each percent to a decimal.
$3.00156\%$
$0.00034\%$
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