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231 lines
8.5 KiB
HTML
231 lines
8.5 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/calculator-fun.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:45:11 GMT -->
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<title>Calculator Fun</title>
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<article id="content" role="main"><!-- #BeginEditable "Body" -->
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<h1 class="center">Calculator Fun</h1>
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<p>Use your own calculator, or the <a href="../calculator-precision.html">Full Precision Calculator</a> for many more digits.</p>
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<p>Many of these seem like magic, but there is always a reason ... see if you can discover it! </p>
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<p style="float:right; margin: 0 0 5px 10px;">
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<img src="../images/style/calculator.gif" alt="calculator" title="calculator">
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</p>
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<h2>Seven</h2>
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<p>Try this in a calculator: <b>1/7</b></p>
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<p>We get 0.142857142857...</p>
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<p><b>2/7</b> gets 0.285714285714...</p>
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<p> <b>3/7</b> gets 0.428571428571...</p>
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<p>In each case it is the same digits "142857" repeating over and over again, justy starting at a different spot.</p>
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<h2>Nine</h2>
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<p>Try this in a calculator: <b>1/9</b></p>
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<p>We get 0.11111111...</p>
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<p><b>2/9</b> gets 0.22222222...</p>
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<p><b>8/9</b> gets 0.88888888...</p>
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<p><b>9/9</b> gets ?</p>
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<h2>Nines Squared</h2>
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<p>Now try <b>1/9^2</b> (1 divided by 9 squared which equals <b>1/81</b>)</p>
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<p>We get 0.0123456790123...</p>
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<p>All the digits from 0 to 9 repeat over and over again, but '8' is missing! </p>
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<p> </p>
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<p>Now try <b>1/99^2</b> (1 divided by 99 squared which equals <b>1/9801</b>)</p>
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<p>We get 0.0001020304050607080910111213141516171819 etc</p>
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<p>Do you see the decimals are 00,01,02,03,... (but '98' is actually missing)</p>
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<p> </p>
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<p>Now try <b>1/999^2</b> (=<b>1/998001</b>)</p>
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<p>We get 0.000001002003004005006007008009010011012 etc</p>
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<p>the decimals are 000,001,002,003,... (but '998' is actually missing)</p>
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<p></p>
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<h2>Eighty Nine</h2>
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<p>1/89 = 0.01123595505617977528089887640449438202247191<i>0112...</i></p>
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<p>The first few digits (0,1,1,2,3,5) are the <a href="fibonacci-sequence.html">Fibonacci sequence</a></p>
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<p>In a way they <b>all</b> are, except multiple digit numbers (13, 21, etc) <b>overlap</b>, like this:</p>
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<table align="center" border="0">
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<tbody>
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<tr>
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<td>0.0</td>
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</tr>
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<tr>
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<td>0.01</td>
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</tr>
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<tr>
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<td>0.001</td>
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</tr>
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<tr>
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<td>0.0002</td>
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</tr>
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<tr>
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<td>0.00003</td>
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</tr>
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<tr>
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<td>0.000005</td>
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</tr>
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<tr>
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<td>0.0000008</td>
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</tr>
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<tr>
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<td>0.00000013</td>
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</tr>
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<tr>
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<td>0.000000021</td>
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</tr>
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<tr>
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<td> ... etc ...</td>
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</tr>
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<tr>
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<td style="border-top: 2px solid black"><br></td>
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</tr>
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<tr>
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<td><b>0.011235955056179775...</b> = 1/89</td>
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</tr>
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</tbody></table>
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<h2>Seven Again<br>
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</h2>
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<p>Try this in a calculator: <b>1/7^2</b></p>
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<p>We get 0.02040816326530...</p>
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<p>Notice how every two digits <b>double </b>each time: 2, 4, 8, 16, 32, 64 (well 65, because it is being overwritten with the next number 128 similar to the above)</p>
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<p>Now try <b>1/49999</b> on the <a href="../calculator-precision.html">Full Precision Calculator</a> to see what you get.</p>
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<h2>Ends With Seven Magic</h2>
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<p>Type in a random 3 digit number twice</p>
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<p>Example: start with 638, so enter <b>638638</b></p>
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<p>Now divide by 11: 638638 / 11 = 58058</p>
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<p>Now divide by 13: 58058 / 13 = 4466</p>
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<p>Then divide by the original number: 4466 / 638 = 7 </p>
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<p>You will <b>always end with 7</b></p>
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<h2>Ends With Seventy Three Magic</h2>
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<p>Type in a random 4 digit number twice</p>
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<p>Example: start with 6385m so enter <b>63856385</b></p>
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<p>Now divide by 137: 63856385 / 137 = 466105</p>
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<p>Then divide by the original number: 466105 / 6385 = 73</p>
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<p>You will <b>always end with 73</b></p>
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<h2>Guess the Number</h2>
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<p>Ask someone to choose a number between 1 and 9</p>
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<p>Have them multiply their number by 12345679 (no 8 OK) and they will have a big number like 86419753. Now ask them to give you the calculator.</p>
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<p>You then multply that number by 9 (let them see you only press a few buttons), and you will see a number like 777777777, which means their chosen number was 7</p>
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<h2>Guess The Numbers</h2>
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<p>Get a friend to choose two numbers between 1 and 9</p>
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<p>Get them to multiply one of them by 5, then add 7, then multiply all of that by 2</p>
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<p>Now get them to add their other number, and announce the result.</p>
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<p>You can now subtract 14 and the two digit number remaining is the two original numbers next to each other</p>
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<p>Example: 4 and 9</p>
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<p>They calculate: 4 x 5 = 20, + 7 = 27, x 2 = 54, + 9 = 63.</p>
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<p>You subtract 14 from that and get 49. You can then say "your original numbers were 4 and 9". </p>
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<h2>Calculator Words</h2>
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<p class="center"><img src="images/calculator-fun.svg" alt="hello"></p>
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<p>Do the calculation, then rotate the display 180°:</p>
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<ul>
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<li>206 × 3 <span class="hide1">BIG</span></li>
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<li>454 × 17 <span class="hide1">BILL</span></li>
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<li>13 × 26 <span class="hide1">BEE</span></li>
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<li>1 − 0.98 <span class="hide1">ZOO</span></li>
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<li>101 × 8 <span class="hide1">BOB</span></li>
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<li>1 − 0.2266 <span class="hide1">HELLO</span></li>
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<li>333 + 204 <span class="hide1">LES</span></li>
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<li>101 × 7 <span class="hide1">LOL</span></li>
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<li>499 × 155 <span class="hide1">SHELL</span></li>
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<li>115469 × 5 <span class="hide1">SHELLS</span></li>
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<li>819 × 7 <span class="hide1">EELS</span></li>
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<li>5555 + 82 <span class="hide1">LEGS</span></li>
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<li>0.0113 × 7 <span class="hide1">IGLOO</span></li>
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<li>73 × 106 <span class="hide1">BELL</span></li>
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<li>0.18 + 0.19 <span class="hide1">LEO</span></li>
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<li>68 × 81 <span class="hide1">BOSS</span></li>
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<li>1102 × 7<span class="hide1">HILL</span></li>
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<li>5001 × 7<span class="hide1">LOOSE</span></li>
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<li>27689 × 2<span class="hide1">BLESS</span></li>
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<li>1262 × 28<span class="hide1">GEESE</span></li>
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<li>10238 × 37 <span class="hide1">GOBBLE</span></li>
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</ul>
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<p> </p>
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<div class="related"><a href="index.html">Number Index</a></div>
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Copyright © 2019 MathsIsFun.com
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