document.write( "Question 297839: How do you write the repeating decimal 0.2424.... as a quotient of integers? \n" ); document.write( "

Algebra.Com's Answer #214477 by Edwin McCravy(20056) $\"\"$ $\"About$

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How do you write the repeating decimal 0.2424.... as a quotient of integers?
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document.write( " N = 0.24242424242424....\r\n" );
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document.write( "Now since there are 2 digits that repeat multiply both sides \r\n" );
document.write( "by  or 100\r\n" );
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document.write( "100N = 24.242424242424....\r\n" );
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document.write( "Now write the first equation underneath the second equation,\r\n" );
document.write( "linng up the decimal points:\r\n" );
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document.write( "100N = 24.242424242424....\r\n" );
document.write( "   N =  0.24242424242424....\r\n" );
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document.write( "Now subtract:\r\n" );
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document.write( "100N = 24.242424242424....\r\n" );
document.write( "   N =  0.24242424242424....\r\n" );
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document.write( " 99N = 24.00000000000000...\r\n" );
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document.write( "So you see the decimals all cancel out\r\n" );
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document.write( " 99N = 24\r\n" );
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document.write( "Divide both sides by 99\r\n" );
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document.write( "Now simplify and reduce the fraction:\r\n" );
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document.write( "Check by dividing 8 by 33 and the get 0.2424242424...\r\n" );
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document.write( "A short cut is to put the repeating digits over a number\r\n" );
document.write( "that has that many 9's as its only digits and reduce if possible.\r\n" );
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document.write( "For example, to change this to a quotient of integers:\r\n" );
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document.write( "0.972972972972...\r\n" );
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document.write( "Put 972 over 999\r\n" );
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document.write( " reduce the fraction to \r\n" );
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document.write( "Edwin

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