<h2>Using the Definition of Percent</h2>
<p>How many cents are in one dollar? There are \(100\) cents in a dollar. How many years are in a century? There are \(100\) years in a century. Does this give you a clue about what the word “percent” means? It is really two words, “per cent,” and means per one hundred. A <strong>percent</strong> is a ratio whose denominator is \(100.\) We use the percent symbol \(\text{%,}\) to show percent.</p>
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<h3>Definition: Percent</h3>
<p>A percent is a ratio whose denominator is \(100.\)</p>
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<p>According to data from the American Association of Community Colleges \(\left(2015\right)\text{,}\) about \(\text{57%}\) of community college students are female. This means \(57\) out of every \(100\) community college students are female, as the figure below shows. Out of the \(100\) squares on the grid, \(57\) are shaded, which we write as the ratio \(\frac{57}{100}.\)</p>
<div class="wp-caption alignnone" style="width: 177px"><img alt="The figure shows a hundred flat with 57 units shaded." height="177" src="https://data.ulearngo.com/assets/aed051f7-244c-4d53-8023-1185b21cc8ec" width="177"/><p class="wp-caption-text">Among every \(100\) community college students, \(57\) are female.</p></div>
<p>Similarly, \(\text{25%}\) means a ratio of \(\frac{25}{100},\text{3%}\) means a ratio of \(\frac{3}{100}\) and \(\text{100%}\) means a ratio of \(\frac{100}{100}.\) In words, "one hundred percent" means the total \(\text{100%}\) is \(\frac{100}{100},\) and since \(\frac{100}{100}=1,\) we see that \(\text{100%}\) means \(1\) whole.</p>
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<h2>Example</h2>
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<p>According to the Public Policy Institute of California \(\left(2010\right)\text{,}\phantom{\rule{0.2em}{0ex}}\text{44%}\) of parents of public school children would like their youngest child to earn a graduate degree. Write this percent as a ratio.</p>
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<h3>Solution</h3>
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<td>The amount we want to convert is 44%.</td>
<td>\(44%\)</td>
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<td>Write the percent as a ratio. Remember that <em>percent</em> means per 100.</td>
<td>\(\frac{44}{100}\)</td>
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<h2>Example</h2>
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<p>In \(2007,\) according to a U.S. Department of Education report, \(21\) out of every \(100\) first-time freshmen college students at \(\text{4-year}\) public institutions took at least one remedial course. Write this as a ratio and then as a percent.</p>
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<h3>Solution</h3>
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<td>The amount we want to convert is \(21\) out of \(100\).</td>
<td>\(21\) out of \(100\)</td>
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<td>Write as a ratio.</td>
<td>\(\frac{21}{100}\)</td>
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<td>Convert the 21 per 100 to percent.</td>
<td>\(21%\)</td>
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Using the Definition of Percent

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.


Using the Definition of Percent

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