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<h2>Converting Percents to Fractions and Decimals</h2>
<p>Since percents are ratios, they can easily be expressed as fractions. Remember that <strong>percent</strong> means per \(100,\) so the denominator of the fraction is \(100.\)</p>
<div class="ns-tutorial">
<div class="ns-school-defn2">
<h3>How to Convert a percent to a fraction.</h3>
<ol type="1">
<li>Write the percent as a ratio with the denominator \(100.\)</li>
<li>Simplify the fraction if possible.</li>
</ol>
</div>
</div>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<div data-type="example">
<div>
<div>
<p>Convert each percent to a fraction:</p>
<ol type="1">
<li>\(\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}\text{36%}\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}\)</li>
<li>\(\phantom{\rule{0.2em}{0ex}}\text{125%}\)</li>
</ol>
</div>
<div>
<h3>Solution</h3>
<table data-label="" summary=".">
<tbody>
<tr>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td>\(36%\)</td>
</tr>
<tr>
<td>Write as a ratio with denominator 100.</td>
<td>\(\frac{36}{100}\)</td>
</tr>
<tr>
<td>Simplify.</td>
<td>\(\frac{9}{25}\)</td>
</tr>
</tbody>
</table>
<table data-label="" summary=".">
<tbody>
<tr>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td>\(125%\)</td>
</tr>
<tr>
<td>Write as a ratio with denominator 100.</td>
<td>\(\frac{125}{100}\)</td>
</tr>
<tr>
<td>Simplify.</td>
<td>\(\frac{5}{4}\)</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
</div>
<p>The previous example shows that a <strong>percent</strong> can be greater than \(1.\) We saw that \(\text{125%}\) means \(\frac{125}{100},\) or \(\frac{5}{4}.\) These are improper fractions, and their values are greater than one.</p>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<div data-type="example">
<div>
<div>
<p>Convert each percent to a fraction:</p>
<ol type="1">
<li>\(\phantom{\rule{0.2em}{0ex}}\text{24.5%}\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}\)</li>
<li>\(\phantom{\rule{0.2em}{0ex}}33\frac{1}{3}%\)</li>
</ol>
</div>
<div>
<h3>Solution</h3>
<table data-label="" summary=".">
<tbody>
<tr>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td>\(24.5%\)</td>
</tr>
<tr>
<td>Write as a ratio with denominator 100.</td>
<td>\(\frac{24.5}{100}\)</td>
</tr>
<tr>
<td>Clear the decimal by multiplying numerator and denominator by 10.</td>
<td>\(\frac{24.5\left(10\right)}{100\left(10\right)}\)</td>
</tr>
<tr>
<td>Multiply.</td>
<td>\(\frac{245}{1000}\)</td>
</tr>
<tr>
<td>Rewrite showing common factors.</td>
<td>\(\frac{5·49}{5·200}\)</td>
</tr>
<tr>
<td>Simplify.</td>
<td>\(\frac{49}{200}\)</td>
</tr>
</tbody>
</table>
<table data-label="" summary=".">
<tbody>
<tr>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td>\(33\frac{1}{3}%\)</td>
</tr>
<tr>
<td>Write as a ratio with denominator 100.</td>
<td>\(\frac{33\frac{1}{3}}{100}\)</td>
</tr>
<tr>
<td>Write the numerator as an improper fraction.</td>
<td>\(\frac{\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}\frac{100}{3}\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}}{100}\)</td>
</tr>
<tr>
<td>Rewrite as fraction division, replacing 100 with \(\frac{100}{1}\).</td>
<td>\(\frac{100}{3}÷\frac{100}{1}\)</td>
</tr>
<tr>
<td>Multiply by the reciprocal.</td>
<td>\(\frac{100}{3}\cdot \frac{1}{100}\)</td>
</tr>
<tr>
<td>Simplify.</td>
<td>\(\frac{1}{3}\)</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
</div>
<p>In <a data-page="29" href="https://app.ulearngo.com/tutorial/mathematics-105/">Mathematics 105</a>, we learned how to convert fractions to decimals. To convert a percent to a decimal, we first convert it to a fraction and then change the fraction to a decimal.</p>
<div class="ns-tutorial">
<div class="ns-school-defn2">
<h3>How to Convert a percent to a decimal.</h3>
<ol type="1">
<li>Write the percent as a ratio with the denominator \(100.\)</li>
<li>Convert the fraction to a decimal by dividing the numerator by the denominator.</li>
</ol>
</div>
</div>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<div data-type="example">
<div>
<div>
<p>Convert each percent to a decimal:</p>
<ol type="1">
<li>\(\phantom{\rule{0.4em}{0ex}}\text{6%}\phantom{\rule{0.4em}{0ex}}\)</li>
<li>\(\phantom{\rule{0.2em}{0ex}}\text{78%}\)</li>
</ol>
</div>
<div>
<h3>Solution</h3>
<p>Because we want to change to a decimal, we will leave the fractions with denominator \(100\) instead of removing common factors.</p>
<table data-label="" summary=".">
<tbody>
<tr>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td>\(6%\)</td>
</tr>
<tr>
<td>Write as a ratio with denominator 100.</td>
<td>\(\frac{6}{100}\)</td>
</tr>
<tr>
<td>Change the fraction to a decimal by dividing the numerator by the denominator.</td>
<td>\(0.06\)</td>
</tr>
</tbody>
</table>
<table data-label="" summary=".">
<tbody>
<tr>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td>\(78%\)</td>
</tr>
<tr>
<td>Write as a ratio with denominator 100.</td>
<td>\(\frac{78}{100}\)</td>
</tr>
<tr>
<td>Change the fraction to a decimal by dividing the numerator by the denominator.</td>
<td>\(0.78\)</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
</div>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<div data-type="example">
<div>
<div>
<p>Convert each percent to a decimal:</p>
<ol type="1">
<li>\(\phantom{\rule{0.3em}{0ex}}\text{135%}\phantom{\rule{0.3em}{0ex}}\)</li>
<li>\(\phantom{\rule{0.3em}{0ex}}\text{12.5%}\)</li>
</ol>
</div>
<div>
<h3>Solution</h3>
<table data-label="" summary=".">
<tbody>
<tr>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td>\(135%\)</td>
</tr>
<tr>
<td>Write as a ratio with denominator 100.</td>
<td>\(\frac{135}{100}\)</td>
</tr>
<tr>
<td>Change the fraction to a decimal by dividing the numerator by the denominator.</td>
<td>\(1.35\)</td>
</tr>
</tbody>
</table>
<table data-label="" summary=".">
<tbody>
<tr>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td>\(12.5%\)</td>
</tr>
<tr>
<td>Write as a ratio with denominator 100.</td>
<td>\(\frac{12.5}{100}\)</td>
</tr>
<tr>
<td>Change the fraction to a decimal by dividing the numerator by the denominator.</td>
<td>\(0.125\)</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
</div>
<p>Let's summarize the results from the previous examples in the table below, and look for a pattern we could use to quickly convert a percent number to a decimal number.</p>
<table summary="The table shows two columns and five rows. The  first row is a header row and it labels each column “Percent” and “Decimal”. Under the “Percent” column are the values: 6%, 78%, 135%, 12.5%. Under the “Decimal” column are the values: 0.06, 0.78, 1.35, 0.125.">
<thead>
<tr>
<th>Percent</th>
<th>Decimal</th>
</tr>
</thead>
<tbody>
<tr>
<td>\(\text{6%}\)</td>
<td>\(0.06\)</td>
</tr>
<tr>
<td>\(\text{78%}\)</td>
<td>\(0.78\)</td>
</tr>
<tr>
<td>\(\text{135%}\)</td>
<td>\(1.35\)</td>
</tr>
<tr>
<td>\(\text{12.5%}\)</td>
<td>\(0.125\)</td>
</tr>
</tbody>
</table>
<p>Do you see the pattern?</p>
<p>To convert a <strong>percent</strong> number to a decimal number, we move the decimal point two places to the left and remove the \(%\) sign. (Sometimes the decimal point does not appear in the percent number, but just like we can think of the integer \(6\) as \(6.0,\) we can think of \(\text{6%}\) as \(\text{6.0%}.\)) Notice that we may need to add zeros in front of the number when moving the decimal to the left.</p>
<p>The figure below uses the percents in the table above and shows visually how to convert them to decimals by moving the decimal point two places to the left.</p>
<p><img alt="The figures shows two columns and five rows . The  first row is a header row and it labels each column “Percent” and “Decimal”. Under the “Percent” column are the values: 6%, 78%, 135%, 12.5%. Under the “Decimal” column are the values: 0.06, 0.78, 1.35, 0.125. There are two jumps for each percent to show how to convert it to a decimal." src="https://data.ulearngo.com/assets/42ef8693-10f8-4bc2-9286-d12246f49350"/></p>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<div data-type="example">
<div>
<div>
<p>Among a group of business leaders, \(\text{77%}\) believe that poor math and science education in the U.S. will lead to higher unemployment rates.</p>
<p>Convert the percent to: a fraction a decimal</p>
</div>
<div>
<h3>Solution</h3>
<table data-label="" summary=".">
<tbody>
<tr>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td>\(77%\)</td>
</tr>
<tr>
<td>Write as a ratio with denominator 100.</td>
<td>\(\frac{77}{100}\)</td>
</tr>
</tbody>
</table>
<table data-label="" summary=".">
<tbody>
<tr>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td>\(\frac{77}{100}\)</td>
</tr>
<tr>
<td>Change the fraction to a decimal by dividing the numerator by the denominator.</td>
<td>\(0.77\)</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
</div>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<div data-type="example">
<div>
<div>
<p>There are four suits of cards in a deck of cards—hearts, diamonds, clubs, and spades. The probability of randomly choosing a heart from a shuffled deck of cards is \(\text{25%}.\) Convert the percent to:</p>
<ol type="1">
<li>a fraction</li>
<li>a decimal</li>
</ol>
<div class="wp-caption alignnone" style="width: 450px"><img alt="The figure shows someone holding a deck of cards." height="338" src="https://data.ulearngo.com/assets/29880dd4-fe78-4f4e-997c-25db019f4744" width="450"/><p class="wp-caption-text">(credit: Riles32807, Wikimedia Commons)</p></div>
</div>
<div>
<h3>Solution</h3>
<table data-label="" summary=".">
<tbody>
<tr>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td>\(25%\)</td>
</tr>
<tr>
<td>Write as a ratio with denominator 100.</td>
<td>\(\frac{25}{100}\)</td>
</tr>
<tr>
<td>Simplify.</td>
<td>\(\frac{1}{4}\)</td>
</tr>
</tbody>
</table>
<table data-label="" summary=".">
<tbody>
<tr>
<td> </td>
<td>\(\frac{1}{4}\)</td>
</tr>
<tr>
<td>Change the fraction to a decimal by dividing the numerator by the denominator.</td>
<td>\(0.25\)</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
</div>

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Converting Percents to Fractions and Decimals

Mathematics studies measurement, relationships, and properties of quantities and sets, using numbers and symbols. Arithmetic, algebra, geometry, and calculus are popular topics in mathematics.

Mathematics

Explore concepts such as converting between fractions, decimals and percentages, solving percentage-related applications and word problems, and using proportion to solve percentage equations.


Converting Percents to Fractions and Decimals

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