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470 lines
18 KiB
HTML
470 lines
18 KiB
HTML
<!DOCTYPE html>
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<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
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<!-- Mirrored from www.mathsisfun.com/measure/metric-system.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:49:31 GMT -->
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<title>Metric System of Measurement</title>
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<script language="JavaScript" type="text/javascript">
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reSpell = [
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["liter", "litre"],
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["liters", "litres"],
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["megaliter", "megalitre"],
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["meter", "metre"],
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["meters", "metres"],
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["millimeter", "millimetre"],
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["kilometer", "kilometre"],
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["kilometers", "kilometres"]
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];
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</script>
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<meta name="Description" content="The metric system is a system of measuring based on the meter, kilogram and second">
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<meta name="keywords" content="math, maths, mathematics, school, homework, education">
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<body id="bodybg">
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<div id="stt"></div>
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<div id="adTop"></div>
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<header>
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<div id="hdr"></div>
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<div id="tran"></div>
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<div id="adHide"></div>
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<div id="cookOK"></div>
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<div id="logo"><a href="../index.html"><img src="../images/style/logo.svg" alt="Math is Fun"></a></div>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Metric System of Measurement</h1>
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<p class="center"><i>(Correctly called "<a href="#si">SI</a>")</i></p>
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<p>The metric system is a <b>system of measuring</b>. It has three main units:</p>
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<table align="center" cellspacing="5" border="0">
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<tbody>
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<tr style="text-align:center;">
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<td><span class="large">m</span></td>
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<td> </td>
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<td>the <b>meter</b> for length </td>
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</tr>
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<tr style="text-align:center;">
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<td><span class="large">kg</span></td>
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<td> </td>
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<td>the <b>kilogram</b> for mass</td>
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</tr>
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<tr style="text-align:center;">
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<td><span class="large">s</span></td>
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<td> </td>
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<td>the <b>second</b> for time</td>
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</tr>
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</tbody></table>
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<div class="center larger">
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<div class="center80">With those three simple measurements<br>
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we can measure <i>nearly everything</i> in the world!</div>
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</div>
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<h2>Examples:</h2>
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<h3>Meter</h3>
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<p class="center">The <a href="metric-length.html">length</a> of this guitar
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is about <b>1 meter</b>:<br>
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<img src="images/guitar-length.jpg" alt="1 meter" height="172" width="259"></p>
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<p class="center">When unfolded this ruler measures <b>2 meters</b>:<br>
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<img src="images/carpenters-rule.jpg" alt="ruler" height="111" width="156"></p>
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<p><br></p>
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<h3>Kilogram</h3>
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<p class="center">This gold bar has a <a href="metric-mass.html">mass</a> of <b>1 kilogram</b>:<br>
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<img src="../definitions/images/gold-1kg.jpg" alt="1 kilogram" height="212" width="220"></p>
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<p class="center">A dictionary also has a mass of about <b>1 kilogram</b>:<br>
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<img src="images/dictionary.jpg" alt="Dictionary" height="81" width="113"></p>
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<p><br></p>
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<h3>Second</h3>
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<div class="center"><b>1 second</b> is about as long as it takes to say <i>"one thousand one"</i><br>
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<div class="script" style="height: 300px;">
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images/clock-drag.js?w=300
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</div>
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</div>
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<!--<script>putFlash6(228,224,'images/clock-analog-seconds.swf','','#FFFFFF');</script>
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<noscript>
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<object classid="clsid:d27cdb6e-ae6d-11cf-96b8-444553540000" codebase="https://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=7,0,0,0" width="228" height="224" id="images/clock-analog-seconds.swf" align="middle">
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<param name="allowScriptAccess" value="sameDomain" /><param name="movie" value="images/clock-analog-seconds.swf" /><param name="quality" value="high" /></object>
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</noscript>
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-->
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<h2>Larger or Smaller</h2>
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<p class="center large">But what if we want to talk about really big or really small things?</p>
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<p class="larger">Answer: we can use <a href="../metric-numbers.html">Metric Number Prefixes</a></p>
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<ul>
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<li>like "kilo" (a thousand)</li>
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<li>and "milli" (one thousandth)</li>
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<li>and so on</li>
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</ul>
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<div class="example">
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<h3>Examples:</h3>
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<p>something that is 1,000 meters is a "<b>kilo</b>meter"</p>
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<p>a very short time of <b>one thousandth</b> of a second is a "<b>milli</b>second"</p>
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</div>
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<div class="center80">
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<p>In fact the kilogram already uses this method, as it's a <b>thousand grams</b>, a <b>kilo</b>gram.</p>
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</div>
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<p>Here is a quick summary of the special prefixes:</p>
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<h2 align="center">Common Big and Small Numbers</h2>
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<div class="simple">
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<table align="center" cellspacing="2" cellpadding="4" border="0">
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<tbody>
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<tr>
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<th style="text-align:center;"><b>Name</b></th>
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<th style="text-align:center;"><b>The
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Number</b></th>
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<th class="large" align="center"><b>Prefix</b></th>
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<th style="text-align:center;"><b>Symbol</b></th>
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</tr>
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<tr>
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<td style="text-align:center;">trillion</td>
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<td style="text-align:right;">1,000,000,000,000</td>
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<td class="large" align="center">tera</td>
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<td style="text-align:center;">T</td>
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</tr>
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<tr>
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<td style="text-align:center;">billion</td>
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<td style="text-align:right;">1,000,000,000</td>
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<td class="large" align="center">giga</td>
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<td style="text-align:center;">G</td>
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</tr>
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<tr>
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<td style="text-align:center;">million</td>
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<td style="text-align:right;">1,000,000</td>
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<td class="large" align="center">mega</td>
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<td style="text-align:center;">M</td>
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</tr>
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<tr>
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<td style="text-align:center;">thousand</td>
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<td style="text-align:right;">1,000</td>
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<td class="large" align="center">kilo</td>
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<td style="text-align:center;">k</td>
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</tr>
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<tr>
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<td style="text-align:center;">hundred</td>
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<td style="text-align:right;">100</td>
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<td class="large" align="center">hecto</td>
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<td style="text-align:center;">h</td>
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</tr>
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<tr>
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<td style="text-align:center;">ten</td>
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<td style="text-align:right;">10</td>
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<td class="large" align="center">deka</td>
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<td style="text-align:center;">da</td>
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</tr>
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<tr align="center">
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<td style="text-align:center;"><b>unit</b></td>
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<td><b>1</b></td>
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<td><br></td>
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<td><br></td>
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</tr>
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<tr>
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<td style="text-align:center;">tenth</td>
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<td>0.1</td>
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<td class="large" align="center">deci</td>
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<td style="text-align:center;">d</td>
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</tr>
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<tr>
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<td style="text-align:center;">hundredth</td>
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<td>0.01</td>
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<td class="large" align="center">centi</td>
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<td style="text-align:center;">c</td>
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</tr>
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<tr>
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<td style="text-align:center;">thousandth</td>
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<td>0.001</td>
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<td class="large" align="center">milli</td>
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<td style="text-align:center;">m</td>
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</tr>
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<tr>
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<td style="text-align:center;">millionth</td>
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<td>0.000 001</td>
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<td class="large" align="center">micro</td>
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<td style="text-align:center;">µ</td>
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</tr>
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<tr>
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<td style="text-align:center;">billionth</td>
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<td>0.000 000 001</td>
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<td class="large" align="center">nano</td>
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<td style="text-align:center;">n</td>
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</tr>
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<tr>
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<td style="text-align:center;">trillionth</td>
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<td>0.000 000 000 001</td>
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<td class="large" align="center">pico</td>
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<td style="text-align:center;">p</td>
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</tr>
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</tbody></table>
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</div>
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<div class="example">
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<h3>Examples:</h3>
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<p>A thousand meters is a kilometer and abbreviated <b>km</b> (k for kilo, m for meter)</p>
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<p>A million liters is a megaliter and abbreviated <b>ML</b></p>
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<p>A millionth of a second is a microsecond and abbreviated <b>µs</b> (µ is the greek symbol "mu")</p>
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</div>
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<p>These prefixes are used for computers too! A megabyte (MB) is a million bytes, a gigabyte (GB) is a billion bytes, etc.</p>
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<div class="words">
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<p><b>How to remember?</b></p>
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<p>For large values (each one a thousand times bigger) say:</p>
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<p class="center larger">"kilo mega giga tera"</p>
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<p>And for small values (each one a thousand times smaller) say:</p>
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<p class="center larger">"milli micro nano pico"</p> Try saying them both a few times, they sort of rhyme and become easy to remember.</div>
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<h2>Making Other Units</h2>
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<p>We can also <b>combine</b> the meter, kilogram and second to make new <a href="unit.html">Units of Measurement</a>!</p>
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<div class="example">
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<h3>Example: Speed</h3>
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<p>Speed is how <b>far</b> something moves over a period of <b>time</b></p>
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<p>So it can be measured in <b>meters</b> per <b>second</b></p>
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<p>It means: <b>How many meters does something travel in one second</b></p>
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<p>We can write it as <span class="large">meters/second</span>, or more simply <span class="large">m/s</span></p>
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</div>
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<p>Here are a few common units that are based on the <b>meter</b>, <b>kilogram</b> and <b>second</b>:</p>
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<h2>Area</h2>
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<h3>Square Meter</h3>
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<div class="indent50px">
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<div style="float:left; margin: 0 20px 5px 0;"><img src="../geometry/images/regular-quadrilateral-sm.gif" alt="square" height="40" width="40"></div>
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<p><a href="../area-conversion.html">Area</a> is length by length, so the basic unit of area is a square that is 1 meter on each side, in other words one square meter.</p>
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<p>The Unit is <span class="large">meters × meters</span>, which is written <span class="large">m<sup>2</sup></span></p>
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</div>
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<div style="clear: left"></div>
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<h2>Volume</h2>
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<h3>Cubic Meter</h3>
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<div class="indent50px">
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<div style="float:left; margin: 0 20px 5px 0;"><img src="../geometry/images/poly-cube.svg" alt="cube" height="68" width="68"></div>
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<p><a href="../volume-conversion.html">Volume</a> is length by length by length, so the basic unit of volume is a <b>cube that is 1 meter on each side</b>, in other words one cubic meter.</p>
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<p>The Unit is <span class="large">meters × meters</span><span class="large"> × meters</span>, which is written <span class="large">m<sup>3</sup></span></p>
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</div>
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<div style="clear: left"></div>
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<h3>Liter</h3>
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<div class="indent50px">
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<p>A cube that is 1 meter on each side is also <b>equal to 1,000 liters</b>.</p>
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<p class="center large">1 m<sup>3</sup> = 1,000 Liters</p>
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<p>Liter is abbreviated <b>L</b> (some people use lowercase <b>l</b>, but that looks too much like <b>1</b>).</p>
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<p>So a liter is actually <b>one-thousandth</b> of a cubic meter.</p>
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<div class="frac">
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<p class="center large">1 Liter = <span class="intbl"><em>1</em><strong>1000</strong></span> m<sup>3</sup></p>
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</div>
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<p>Another way of thinking about a liter is:</p>
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<ul>
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<li>A box that is 0.1 meters (10 cm) on each side,</li>
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<li>One square meter that is millimeter thick.</li>
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</ul>
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</div>
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<h2>Time</h2>
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<h3>Hour</h3>
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<div class="indent50px">
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<p>An hour is 60 minutes, and a minute is 60 seconds, so an hour is:</p>
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<ul>
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<li>60 × 60 = 3,600 seconds</li>
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</ul>
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</div>
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<h3>Day</h3>
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<div class="indent50px">
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<p>A day is 24 hours so:</p>
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<ul>
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<li>1 day = 24 × 60 × 60 = 86,400 second</li>
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</ul>
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</div>
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<h2>Speed</h2>
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<h3>Speed in meters per second (m/s)</h3>
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<div class="indent50px">
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<div style="float:left; margin: 0 20px 5px 0;"><img src="../images/pat-athlete.gif" alt="square" height="86" width="51"></div>
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<p>This is a combination of two units (meters and seconds) to make a new one (m/s).</p>
|
||
<p>If something is moving at 1 m/s it moves <b>1 meter every second</b>.</p>
|
||
</div>
|
||
<div style="clear: left"></div>
|
||
|
||
<h3>Speed in kilometers per hour (km/h)</h3>
|
||
<div class="indent50px">
|
||
<p>A kilometer has 1000 meters, and an hour has 3600 seconds, so a kilometer per hour is:</p>
|
||
<ul>
|
||
<li>1000 / 3600 = 1/3.6 = 0.277... m/s</li>
|
||
</ul>
|
||
<p>How did I know to make it <b>1000/3600</b>, and not 3600/1000 (the other way around)? Read how to <a href="unit-conversion-method.html">Safely Convert From One Unit to Another</a>.</p>
|
||
</div>
|
||
|
||
|
||
<h2>Acceleration</h2>
|
||
|
||
<div class="indent50px">
|
||
<p><a href="metric-acceleration.html">Acceleration</a> is how fast velocity changes.</p>
|
||
<p>When a runner accelerates from <b>5 m/s</b> (5 meter per second) to <b>6 m/s</b> (6 meters per second) <i>in just one second</i>, they accelerate by <b>1 meter per second <i>per second</i></b>!</p>
|
||
<p>And yes, "per second" is used twice!<br>
|
||
It can be thought of as (m/s)/s but is usually written m/s<sup>2</sup></p>
|
||
</div>
|
||
<p style="float:right; margin: 0 0 5px 10px;"><img src="../physics/images/ball-kick.jpg" alt="Force" height="201" width="360"></p>
|
||
|
||
|
||
<h2>Force</h2>
|
||
|
||
<p><a href="../physics/force.html">Force</a> is usually measured in the Unit of Newtons, an important measurement in Physics and Engineering.</p>
|
||
<p>A Newton is how much force it takes to make <b>1 kg</b> accelerate at <b>1 m/s<sup>2</sup></b>.</p>
|
||
<div style="clear:both"></div>
|
||
<p class="center">1 <b>Newton</b> = 1 <b>kg m/s<sup>2</sup></b> (one kilogram meter per second squared).</p>
|
||
<p class="center larger">So force is actually based on the <b>meter</b>, <b>kilogram</b> and <b>second</b>.</p>
|
||
<p>And so <b>force is a combination of the three basic units</b>.</p>
|
||
|
||
|
||
<h2><a name="si" id="si"></a>SI</h2>
|
||
|
||
<p>The Metric System had its beginnings back in <b>1670</b> by a mathematician called Gabriel Mouton.</p>
|
||
<p>The modern version, (since 1960) is <b>correctly called</b> "International System of Units" or "SI" (from the French "<i><b>S</b>ystème <b>I</b>nternational</i>").</p>
|
||
<p class="center large">So we should really call it "<b>SI</b>", but mostly people just call it "Metric".</p>
|
||
<p>A few special units are also needed to complete the SI System:</p>
|
||
<ul>
|
||
<li>ampere for electric current,</li>
|
||
<li>kelvin for temperature,</li>
|
||
<li>mole for the amount of substance, and</li>
|
||
<li>candela for luminous intensity</li>
|
||
</ul>
|
||
<p>So the complete list is:</p>
|
||
<div class="beach">
|
||
<table align="center" width="80%" border="0">
|
||
<tbody>
|
||
<tr>
|
||
<th align="right" width="25">Quantity</th>
|
||
<th align="right" width="25">Name</th>
|
||
<th align="right" width="25">Symbol</th>
|
||
</tr>
|
||
<tr style="text-align:right;">
|
||
<td>Length</td>
|
||
<td><b>meter</b></td>
|
||
<td>m</td>
|
||
</tr>
|
||
<tr style="text-align:right;">
|
||
<td>Mass</td>
|
||
<td><b>kilogram</b></td>
|
||
<td>kg</td>
|
||
</tr>
|
||
<tr style="text-align:right;">
|
||
<td>Time</td>
|
||
<td><b>second</b></td>
|
||
<td>s</td>
|
||
</tr>
|
||
<tr style="text-align:right;">
|
||
<td> </td>
|
||
<td> </td>
|
||
<td> </td>
|
||
</tr>
|
||
<tr style="text-align:right;">
|
||
<td>Electric Current</td>
|
||
<td><b>ampere</b></td>
|
||
<td>A</td>
|
||
</tr>
|
||
<tr style="text-align:right;">
|
||
<td>Temperature</td>
|
||
<td><b>kelvin</b></td>
|
||
<td>K</td>
|
||
</tr>
|
||
<tr style="text-align:right;">
|
||
<td>Amount of substance</td>
|
||
<td><b>mole</b></td>
|
||
<td>mol</td>
|
||
</tr>
|
||
<tr style="text-align:right;">
|
||
<td>Luminous intensity</td>
|
||
<td><b>candela</b></td>
|
||
<td>cd</td>
|
||
</tr>
|
||
</tbody></table>
|
||
</div>
|
||
<p>All other units (such as <a href="metric-speed.html">speed</a>, <a href="../physics/force.html">force</a>, <a href="../physics/power.html">power</a> and many more) are "derived units" that are defined using these seven base units.</p>
|
||
<p> </p>
|
||
<div class="questions">2204, 2205, 980, 981, 982, 983, 984, 985, 2206, 3609</div>
|
||
|
||
<div class="related">
|
||
<a href="metric-units-details.html">Common Metric Units</a>
|
||
<a href="weight-mass.html">Weight or Mass?</a>
|
||
<a href="../length-conversion.html">How to Convert Lengths</a>
|
||
<a href="../imperial-metric-conversion.html">How to Convert Imperial to Metric</a>
|
||
<a href="../metric-imperial-conversion.html">How to Convert Metric to Imperial</a>
|
||
<a href="../temperature-conversion.html">Converting Temperatures (Celsius and Fahrenheit)</a>
|
||
<a href="../metric-numbers.html">Metric Numbers</a>
|
||
<a href="../unit-conversion-tool.html">Unit Converter</a>
|
||
<a href="index.html">Measurement Index</a>
|
||
</div>
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