Percentages (%)
<h1 align="center">Percentages (%)</h1> <h3 align="center">When we say "Percent" we are really saying "per 100"</h3> <p>One percent (<b>1%</b>) means 1 per 100. </p> <p class="center"><img src="numbers/images/one-in-100.gif" width="690" height="16"><br> <b>1%</b> of this line is shaded green: it is very small isn't it?</p> <p> </p> <div class="centerfull"> <div class="boxleft"> <table border="0"> <tr> <td rowspan="2"><img src="numbers/images/percent-grid-50.gif" alt="50%" width="134" height="134" /></td> <td height="67"><b>50%</b> means 50 per 100<br /> (50% of this box is green) </td> </tr> <tr> <td align="right"><br /></td> </tr> </table> </div> <div class="boxright"> <table border="0"> <tr> <td height="67" align="right"><b>25%</b> means 25 per 100<br /> (25% of this box is green)</td> <td rowspan="2"><img src="numbers/images/percent-grid-25.gif" alt="25%" width="134" height="134" /></td> </tr> <tr> <td align="right"> </td> </tr> </table> </div> </div><div style="clear:both"></div> <h2>Examples:</h2> <table border="0" align="center"> <tr> <td><img src="numbers/images/percent-grid-100.gif" alt="100%" width="134" height="134" /></td> <td align="center"> </td> <td><p>100% means <span class="large">all</span>.</p> <div class="example"> <p>Example:</p> <div class="example2"> <table border="0" align="center"> <tr> <td rowspan="2">100% of <b>80</b> is </td> <td align="center">100</td> <td rowspan="2" align="center"> × 80 = <span class="large">80</span></td> </tr> <tr> <td style="border-top: 1px solid black;">100</td> </tr> </table> </div> </div></td> </tr> <tr> <td><img src="numbers/images/percent-grid-50.gif" alt="50%" width="134" height="134" /></td> <td align="center"> </td> <td><p>50% means <span class="large">half</span>.</p> <div class="example"> <p>Example:</p> <div class="example2"> <table border="0" align="center"> <tr> <td rowspan="2">50% of <b>80</b> is </td> <td align="center">50</td> <td rowspan="2" align="center"> × 80 = <span class="large">40</span></td> </tr> <tr> <td style="border-top: 1px solid black;">100</td> </tr> </table> </div> </div></td> </tr> <tr> <td><img src="numbers/images/percent-grid-5.gif" alt="5%" width="135" height="134" /></td> <td align="center"> </td> <td><p>5% means <span class="frac-large"><sup>5</sup>/<sub>100ths</sub></span>.</p> <div class="example"> <p>Example:</p> <div class="example2"> <table border="0" align="center"> <tr> <td rowspan="2">5% of <b>80</b> is </td> <td align="center">5</td> <td rowspan="2" align="center"> × 80 = <span class="large">4</span></td> </tr> <tr> <td style="border-top: 1px solid black;">100</td> </tr> </table> </div> </div></td> </tr> </table> <h2>Using Percent</h2> <div class="simple"> <table border="0" align="center"> <tr> <td> <div class="flash"> <script type="text/javascript">putFlash6(203,310,'images/percent-slider.swf','','#FFFFFF');</script> <noscript> <object type="application/x-shockwave-flash" width="203" height="310" data="images/percent-slider.swf" align="middle"> <param name="allowScriptAccess" value="sameDomain" /> <param name="allowFullScreen" value="true" /> <param name="movie" value="images/percent-slider.swf" /> <param name="quality" value="high" /> <param name="bgcolor" value="#FFFFFF" /> </object> </noscript> </div> </td> <td valign="top"> <p>Because "Percent" means "per 100" think:</p> <p class="center larger">"this should be divided by 100"<b></b></p> <p>So <b>75%</b> really means <span class="frac"><sup>75</sup>/<sub>100</sub></span></p> <p>And <b>100%</b> is <span class="frac"><sup>100</sup>/<sub>100</sub></span>, or exactly <b>1 </b>(100% of any number is just the number, unchanged)</p> <p>And <b>200%</b> is <span class="frac"><sup>200</sup>/<sub>100</sub></span>, or exactly <b>2 </b>(200% of any number is twice the number)</p></td> </tr> <tr> <td colspan="2">Use the slider on the left side and try some different numbers<br /> (What is 40% of 80? What is 10% of 200? What is 90% of 10?)</td> </tr> </table> </div> <h3>A <b>Percent</b> can also be expressed as a <b><i>Decimal</i></b> or a<i> </i><b><i>Fraction</i></b></h3> <br /> <table border="0" align="center"> <tr> <td><img src="images/fractions/pie-1-2.jpg" width="120" height="120" /></td> <td> </td> <td><table border="0"> <tr> <td><b>A Half</b> can be written...</td> <td> </td> </tr> <tr> <td> </td> <td> </td> </tr> <tr> <td>As a percentage:</td> <td class="large"><div align="center">50%</div></td> </tr> <tr> <td>As a decimal:</td> <td class="large"><div align="center">0.5</div></td> </tr> <tr> <td>As a fraction:</td> <td class="large"><div align="center"><span class="frac"><sup>1</sup>/<sub>2</sub></span></div></td> </tr> </table></td> </tr> </table> <p align="center">Read more about this at <a href="decimal-fraction-percentage.html">Decimals, Fractions and Percentages</a>.</p> <h2>Some Worked Examples</h2> <div class="example"> <h3>Example: Calculate 25% of 80 </h3> <div class="example2"> <table border="0" align="center"> <tr> <td rowspan="2">25% = </td> <td align="center">25</td> </tr> <tr> <td style="border-top: 1px solid black;">100</td> </tr> </table> </div> <div class="example2"> <table border="0" align="center"> <tr> <td rowspan="2">And </td> <td align="center">25</td> <td rowspan="2" align="center"> × 80 = <b>20</b></td> </tr> <tr> <td style="border-top: 1px solid black;">100</td> </tr> </table> </div> <p class="larger">So 25% of 80 is <b>20</b></p> </div> <div class="example"> <h3>Example: 15% of 200 apples were bad. How many apples were bad?</h3> <div class="example2"> <table border="0" align="center"> <tr> <td rowspan="2">15% = </td> <td align="center">15</td> </tr> <tr> <td style="border-top: 1px solid black;">100</td> </tr> </table> </div> <div class="example2"> <table border="0" align="center"> <tr> <td rowspan="2">And </td> <td align="center">15</td> <td rowspan="2" align="center"> × 200 = 15 × </td> <td align="center">200</td> <td rowspan="2" align="center"> = 15 × 2 = <b>30 apples</b></td> </tr> <tr> <td style="border-top: 1px solid black;">100</td> <td style="border-top: 1px solid black;">100</td> </tr> </table> </div> <p><span class="larger"><b>30</b> apples were bad</span></p> </div> <div class="example"> <h3>Example: if only 10 of the 200 apples were bad, what percent is that?</h3> <p>As a fraction, 10/200 = 0.05 </p> <p>As a percentage it is: (10/200) x 100 = 5%</p> <p><span class="larger"><b>5%</b> of those apples were bad</span></p> </div> <div class="example"> <p style="float:left; margin: 0 10px 5px 0;"><img src="numbers/images/skateboard.jpg" width="121" height="73" /></p> <h3>Example: A Skateboard is reduced 25% in price in a sale. <br /> The old price was $120. <br /> Find the new price.</h3> <p> </p> <p>First, find 25% of $120:</p> <div class="example2"> <table border="0" align="center"> <tr> <td rowspan="2">25% = </td> <td align="center">25</td> </tr> <tr> <td style="border-top: 1px solid black;">100</td> </tr> </table> </div> <div class="example2"> <table border="0" align="center"> <tr> <td rowspan="2">And </td> <td align="center">25</td> <td rowspan="2" align="center"> × $120 = <b>$30</b></td> </tr> <tr> <td style="border-top: 1px solid black;">100</td> </tr> </table> </div> <p>25% of $120 is $30</p> <p class="larger">So the <b>reduction</b> is $30</p> <p> </p> <p>Take the reduction from the original price</p> <p class="so"> $120 - $30 = $90</p> <p class="larger">The Price of the Skateboard in the sale is <b>$90</b></p> </div> <h2>The Word</h2> <div class="words">"Percent" comes from the latin <i>Per Centum</i>. The latin word <i>Centum</i> means 100, for example a Century is 100 years.</div> <h2>Percent vs Percentage</h2> <div class="words"> <p>My Dictionary says "Percentage" is the "result obtained by multiplying a quantity by a percent". So 10 <b>percent</b> of 50 apples is 5 apples: the 5 apples is the <b>percentage</b>.</p> <p>But in practice people use both words the same way.</p> </div>
