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356 lines
19 KiB
HTML
356 lines
19 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/place-value.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:44:59 GMT -->
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<head>
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<meta http-equiv="content-type" content="text/html; charset=UTF-8">
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<!-- #BeginEditable "doctitle" -->
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<title>Place Value</title>
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<!-- #EndEditable -->
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<meta name="keywords" content="math, maths, mathematics, school, homework, education">
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<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
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<meta name="HandheldFriendly" content="true">
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<meta name="referrer" content="always">
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<link rel="preload" href="images/style/font-champ-bold.ttf" as="font" type="font/ttf" crossorigin="">
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<link rel="preload" href="style4.css" as="style">
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<link rel="preload" href="main4.js" as="script">
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<link rel="stylesheet" href="style4.css">
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<script src="main4.js" defer="defer"></script>
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<!-- Global site tag (gtag.js) - Google Analytics -->
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<script async="" src="https://www.googletagmanager.com/gtag/js?id=UA-29771508-1"></script>
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<script>
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window.dataLayer = window.dataLayer || [];
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function gtag(){dataLayer.push(arguments);}
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gtag('js', new Date());
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gtag('config', 'UA-29771508-1');
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</script>
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</head>
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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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</header>
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<div class="mid">
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<nav>
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<div id="menuWide" class="menu"></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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<div id="search" role="search"></div>
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<div id="linkto"></div>
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<div id="menuSlim" class="menu"></div>
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<div id="menuTiny" class="menu"></div>
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</nav>
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<div id="extra"></div>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<div class="video">fshyCNqHIbw</div>
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<h1 id="title" align="center">Place Value</h1>
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<p class="center"><i class="larger"> We write numbers using only ten symbols (called Digits).<br>
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Where we place them is important.</i></p>
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<h2>The Ten Digits</h2>
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<p>The Digits we use today are called "Hindu-Arabic Numerals":</p>
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<div class="center largest">0
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1 2 3 4 5 6 7 8 9</div>
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<p><br>
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We can use these on their own to count up to 9:</p>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td class="largest" align="center">0</td>
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<td> </td>
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</tr>
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<tr>
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<td class="largest" align="center" width="80">1</td>
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<td><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"></td>
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</tr>
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<tr>
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<td class="largest" align="center" width="80">2</td>
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<td><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"></td>
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</tr>
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<tr>
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<td class="largest" align="center" width="80">3</td>
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<td><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"></td>
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</tr>
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<tr>
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<td class="largest" align="center" width="80">4</td>
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<td><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"></td>
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</tr>
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<tr>
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<td class="largest" align="center" width="80">5</td>
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<td><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"></td>
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</tr>
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<tr>
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<td class="largest" align="center" width="80">6</td>
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<td><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"></td>
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</tr>
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<tr>
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<td class="largest" align="center" width="80">7</td>
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<td><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"></td>
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</tr>
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<tr>
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<td class="largest" align="center" width="80">8</td>
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<td><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"></td>
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</tr>
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<tr>
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<td class="largest" align="center" width="80">9</td>
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<td><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"></td>
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</tr>
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<tr>
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<td class="largest" align="center" width="80">??</td>
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<td><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"></td>
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</tr>
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</tbody></table>
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<p>But what happens after 9?</p>
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<div class="simple"></div>
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<h2>Ten Or More ...</h2>
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<p>When we have more than 9 items, we start <b>another column</b> - the "tens" column - and we write down
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how many "tens" we have, followed by how many "ones" (also called "units").</p>
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<p>So we write:</p>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td class="center largest hilite" width="80">10</td>
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<td><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"></td>
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</tr>
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</tbody></table>
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<p> </p>
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<div class="example">
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<h3>Example: this is how we write down <b>twelve</b>:</h3>
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<div class="simple">
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr class="bga1">
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<td style="width:80px;">
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<div class="center">Tens</div> </td>
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<td style="width:80px;">
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<div class="center">Ones</div> </td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">1</td>
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<td class="large">2</td>
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</tr>
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<tr style="text-align:center;">
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<td><img src="numbers/images/ball-10.svg" alt="ten balls" height="219" width="22"></td>
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<td><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"></td>
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</tr>
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</tbody></table>
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</div>
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<div class="center large">The Number "12"</div>
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<p class="center"><img src="numbers/images/place-value-12.svg" alt="place value 12 tens ones is 10 2" height="198" width="125"></p>
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<p>It says we have <b>1 Ten</b> and <b>2 Ones</b>, which makes 12.</p>
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<p>This can also be written as <span class="large">1 × 10 + 2 × 1</span>.</p>
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</div>
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<div class="example">
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<h3>Example: "35" means 3 Tens and 5 Ones, which is also 3 × 10 + 5 × 1</h3>
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<div class="simple">
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr class="bga1">
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<td style="width:150px;">
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<div class="center">Tens</div></td>
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<td style="width:150px;">
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<div class="center">Ones</div></td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">3</td>
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<td class="large">5</td>
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</tr>
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<tr style="text-align:center;">
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<td><img src="numbers/images/ball-10.svg" alt="ten balls" height="219" width="22"><img src="numbers/images/ball-10.svg" alt="ten balls" height="219" width="22"><img src="numbers/images/ball-10.svg" alt="ten balls" height="219" width="22"></td>
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<td><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"></td>
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</tr>
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</tbody></table>
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</div>
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<div class="center large">The Number "35"</div>
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</div>
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<h2>Zero</h2>
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<p>What if we have 1 Ten, but no Ones? We show "no Ones" by <b>putting a zero</b> there:</p>
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<div class="simple">
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr class="bga1">
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<td style="width:80px;">
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<div class="center">Tens</div></td>
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<td style="width:80px;">
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<div class="center">Ones</div></td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">1</td>
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<td class="large">0</td>
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</tr>
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<tr style="text-align:center;">
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<td><img src="numbers/images/ball-10.svg" alt="ten balls" height="219" width="22"></td>
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<td> </td>
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</tr>
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</tbody></table>
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</div>
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<div class="center large">The Number "10"</div>
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<p class="center larger">We have to put a Zero in the Ones place or "10" looks like "1".</p>
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<p class="center larger"><img src="numbers/images/place-value-10.svg" alt="place value 10" height="198" width="125"></p>
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<h2>A Hundred Or More ...</h2>
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<p>When we have more than 99 items, we start <b>another</b> column - the "hundreds" column. Now we need
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to show how many Hundreds, Tens and Ones:</p>
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<div class="simple">
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr class="bga1">
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<td>
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<div class="center">Hundreds</div> </td>
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<td>
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<div class="center">Tens</div> </td>
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<td>
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<div class="center">Ones</div> </td>
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</tr>
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<tr style="text-align:center;">
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<td class="large"> 1</td>
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<td class="large"> 4 </td>
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<td class="large"> 3</td>
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</tr>
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<tr style="text-align:center;">
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<td>
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<img src="numbers/images/ball-100.svg" alt="hundred balls" height="219" width="220">
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</td>
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<td><img src="numbers/images/ball-10.svg" alt="ten balls" height="219" width="22"><img src="numbers/images/ball-10.svg" alt="ten balls" height="219" width="22"><img src="numbers/images/ball-10.svg" alt="ten balls" height="219" width="22"><img src="numbers/images/ball-10.svg" alt="ten balls" height="219" width="22"></td>
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<td class="large"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"></td>
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</tr>
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</tbody></table>
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</div>
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<div class="center large">The Number 143</div>
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<p>That shows we have 1 Hundred, 4 Tens and 3 Ones:</p>
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<p>This can also be written as <span class="large">1 × 100 + 4 × 10 + 3 × 1</span>.</p>
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<div class="example">
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<p style="float:right; margin: 0 0 5px 10px;"><img src="numbers/images/place-value-369.svg" alt="place value 369: 300 60 9" height="191" width="166"></p>
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<h3>Example: "369" means 3 Hundreds, 6 Tens and 9 Ones</h3>
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<p>Which is also 3 × 100 + 6 × 10 + 9 × 1</p>
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</div>
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<p>We also use a Zero when there are no Tens:</p>
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<div class="example">
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<h3>Example: "104" means 1 Hundred, <b>Zero</b> Tens and 4 Ones.</h3>
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<div class="simple">
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr class="bga1">
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<td>
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<div class="center">Hundreds</div></td>
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<td>
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<div class="center">Tens</div></td>
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<td>
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<div class="center">Ones</div></td>
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</tr>
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<tr style="text-align:center;">
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<td class="large"> 1</td>
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<td class="large"> 0 </td>
|
||
<td class="large"> 4</td>
|
||
</tr>
|
||
<tr style="text-align:center;">
|
||
<td> <img src="numbers/images/ball-100.svg" alt="hundred balls" height="219" width="220"></td>
|
||
<td> </td>
|
||
<td class="large"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"><img src="numbers/images/ball.svg" alt="one ball" height="22" width="22"></td>
|
||
</tr>
|
||
</tbody></table>
|
||
</div>
|
||
<div class="center large">The Number 104</div>
|
||
</div>
|
||
<h2>And So On ...</h2>
|
||
<p>Each time we want to show a bigger number we just add one column <b>to the left</b> and we know it is always
|
||
<b>10 times bigger</b> than than the column on its right.</p>
|
||
<p class="center"><span class="large">each new column on the left is ten times bigger</span></p>
|
||
<p>So, where we PLACE a digit is important!</p>
|
||
<h2>Names for Each Column</h2>
|
||
<p>These are the names of each column:</p>
|
||
<table style="border: 0; margin:auto;">
|
||
<tbody>
|
||
<tr class="bga1" align="center">
|
||
<td style="width:90px;">Millions</td>
|
||
<td style="width:90px;">Hundred-Thousands</td>
|
||
<td style="width:90px;">
|
||
<div class="center">Ten-Thousands</div></td>
|
||
<td style="width:90px;">
|
||
<div class="center">Thousands</div></td>
|
||
<td style="width:90px;">
|
||
<div class="center">Hundreds</div></td>
|
||
<td style="width:90px;">
|
||
<div class="center">Tens</div></td>
|
||
<td style="width:90px;">
|
||
<div class="center">Ones</div></td>
|
||
</tr>
|
||
</tbody></table>
|
||
<p><i>(For bigger amounts, see <a href="metric-numbers.html">Metric Numbers</a>)</i></p>
|
||
<div class="example">
|
||
<h3>Example: The number eleven thousand, three hundred and twenty seven in a place value table:</h3>
|
||
<div class="simple">
|
||
<table style="border: 0; margin:auto;">
|
||
<tbody>
|
||
<tr class="bga1">
|
||
<td style="width:90px;">
|
||
<div class="center">Ten-Thousands</div> </td>
|
||
<td style="width:90px;">
|
||
<div class="center">Thousands</div> </td>
|
||
<td style="width:90px;">
|
||
<div class="center">Hundreds</div> </td>
|
||
<td style="width:90px;">
|
||
<div class="center">Tens</div> </td>
|
||
<td style="width:90px;">
|
||
<div class="center">Ones</div> </td>
|
||
</tr>
|
||
<tr style="text-align:center;">
|
||
<td class="large"> 1</td>
|
||
<td class="large"> 1</td>
|
||
<td class="large"> 3</td>
|
||
<td class="large"> 2</td>
|
||
<td class="large"> 7</td>
|
||
</tr>
|
||
</tbody></table>
|
||
</div>
|
||
<div class="center large"> The Number 11,327 </div>
|
||
</div>
|
||
<p> </p>
|
||
<div class="questions">1686, 1687, 1688, 1689, 1690, 1691, 5875, 5876, 5877, 5878</div>
|
||
|
||
<div class="related">
|
||
<a href="decimals.html">Decimals</a>
|
||
<a href="decimals-menu.html">Decimals Index</a>
|
||
</div>
|
||
<!-- #EndEditable -->
|
||
|
||
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