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195 lines
6.5 KiB
HTML
195 lines
6.5 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/numbers/zero.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:59:15 GMT -->
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<meta http-equiv="content-type" content="text/html; charset=UTF-8">
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<title>Zero</title>
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<meta name="Description" content="Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.">
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<meta name="keywords" content="math, maths, mathematics, school, homework, education">
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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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<div id="hdr"></div>
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<div id="tran"></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="extra"></div>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Zero</h1>
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<p style="float:left; margin: 0 30px 5px 0;"><img src="images/zero-lg.svg" alt="zero" ></p>
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<p>Zero shows that there is no amount.</p>
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<div class="example">
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<p>Example: <b>6 − 6 = 0</b> (the difference between six and six is zero)</p>
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</div><p> </p>
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<p>It is also used as a "placeholder" so we can write a numeral properly.</p>
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<div class="example">
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<p>Example: <b>502</b> (five hundred and two) could be mistaken for <b>52</b> (fifty two) without the zero in the tens place.</p>
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</div>
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<h2>Zero is a very special number ...</h2>
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<p>It is halfway between −1 and +1 on the <a href="../number-line.html">Number Line</a>:</p>
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<div class="script" style="height: 150px;">
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images/number-line.js?mode=int
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</div>
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<p>Zero is neither negative nor positive. But it is an <a href="even-odd.html">even number</a>.</p>
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<h2>The Idea</h2>
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<p>The idea of <b>zero</b>, though natural to us now, was not natural to early humans ... if there is nothing to count, how can we count it?</p>
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<p class="center"><b>Example: you can count dogs, but you can't count an empty space:</b></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><img src="../sets/images/saluki.jpg" alt="2 dogs" height="112" width="250"></td>
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<td style="width:30px;"> </td>
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<td><img src="../sets/images/saluki-none.jpg" alt="no dogs" height="112" width="250"></td>
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</tr>
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<tr>
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<th>Two Dogs</th>
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<th width="30"> </th>
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<th>Zero Dogs? Zero Cats?</th>
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</tr>
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</tbody></table>
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<p>An empty patch of grass is just an empty patch of grass!</p>
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<h2>Zero as a Placeholder</h2>
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<p>But about 3,000 years ago people needed to tell the difference between numbers like <b>4</b> and <b>40.</b> Without the zero they look the same!</p>
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<p>So zero is now used as a "placeholder": it shows "there is no number at this place", like this:</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="huge">502</td>
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<td style="width:20px;"> </td>
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<td>
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<p>This means 5 hundreds, <b>no tens</b>, and 2 ones</p></td>
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</tr>
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</tbody></table>
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<h2>The Value of Zero</h2>
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<p>Then people started thinking of zero as an actual <b>number</b>.</p>
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<div class="example">
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<h3>Example:</h3>
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<p class="center"><i>"I had 3 oranges, then I ate the 3 oranges, now I have <b>zero</b> oranges...!"</i></p>
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</div>
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<h2>Additive Identity</h2>
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<p>And zero has a special property: when we add it to a number we get that number back, unchanged</p>
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<div class="example">
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<h3>Example:</h3>
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<p class="center larger">7 + 0 = 7</p>
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<p>Adding 0 to 7 gives the answer 7</p>
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<p>Also 0 + 7 = 7</p>
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</div>
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<p>This makes it the <b>Additive Identity</b>, which is just a special way of saying "add 0 and we get the <b>identical</b> (same) number we started with".</p>
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<h2>Special Properties</h2>
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<p>Here are some of zero's properties:</p>
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<div class="simple">
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<table align="center" width="80%" border="0">
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<tbody>
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<tr>
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<th>Property</th>
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<th>Example</th>
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</tr>
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<tr>
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<td>a + 0 = a</td>
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<td>4 + 0 = 4</td>
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</tr>
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<tr>
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<td>a − 0 = a</td>
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<td>4 − 0 = 4</td>
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</tr>
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<tr>
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<td>a × 0 = 0</td>
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<td>6 × 0 = 0</td>
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</tr>
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<tr>
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<td>0 / a = 0</td>
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<td>0/3 = 0</td>
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</tr>
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<tr>
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<td>a / 0 = undefined (<a href="dividing-by-zero.html">dividing by zero is undefined</a>)</td>
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<td>7/0 = undefined</td>
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</tr>
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<tr>
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<td>0<sup>a</sup> = 0 (a is positive)</td>
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<td>0<sup>4</sup> = 0</td>
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</tr>
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<tr>
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<td>0<sup>0</sup> = indeterminate</td>
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<td>0<sup>0</sup> = indeterminate</td>
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</tr>
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<tr>
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<td>0<sup>a</sup> = undefined (a is negative)</td>
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<td>0<sup>-2</sup> = undefined</td>
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</tr>
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<tr>
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<td>0! = 1 ("!" is the <a href="factorial.html">factorial function</a>)</td>
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<td>0! = 1</td>
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</tr>
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</tbody></table>
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</div>
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<p> </p>
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<div class="related">
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<a href="index.html">Numbers Index</a>
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<a href="../algebra/index.html">Algebra Index</a>
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</div>
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</article>
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<div id="copyrt">Copyright © 2021 MathsIsFun.com</div>
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