document.write( "Question 1019496: Hi\r
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Algebra.Com's Answer #635444 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
0.6898989898
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document.write( "Let the fraction be x.  Then\r\n" );
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document.write( "x = 0.6898989898\r\n" );
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document.write( "Since it repeats the 2 digits (\"89\") over and over,\r\n" );
document.write( "we multiply both sides by 102 or 100.\r\n" );
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document.write( "100x = 68.989898989\r\n" );
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document.write( "Now put the original equation underneath that,\r\n" );
document.write( "lining up the decimal points\r\n" );
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document.write( "100x = 68.98989898\r\n" );
document.write( "   x =  0.6898989898\r\n" );
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document.write( "Continue the upper equation so that the decimals go\r\n" );
document.write( "as far as they do on the lower equation, and subtract.\r\n" );
document.write( "Then the string of decimals will cancel:\r\n" );
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document.write( "100x = 68.9898989898\r\n" );
document.write( "   x =  0.6898989898\r\n" );
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document.write( " 99x = 68.3000000000\r\n" );
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document.write( " 99x = 68.3\r\n" );
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document.write( "Now remove the decimal by multiplying both sides by 10\r\n" );
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document.write( "990x = 683\r\n" );
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document.write( "   x = \"683%2F990\"\r\n" );
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document.write( "That doesn't reduce.  Check by dividing out the\r\n" );
document.write( "fraction, changing it back to a decimal\r\n" );
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document.write( "         .6898----\r\n" );
document.write( "  990)683.0000----\r\n" );
document.write( "      594 0\r\n" );
document.write( "       89 00\r\n" );
document.write( "       79 20\r\n" );
document.write( "        9 800\r\n" );
document.write( "        8 910\r\n" );
document.write( "          8900\r\n" );
document.write( "          ....\r\n" );
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document.write( "We don't need to continue because we reached\r\n" );
document.write( "the same remainder 8900 a second time, so\r\n" );
document.write( "the decimals will keep repeating \"89\"\r\n" );
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document.write( "Answer: \"683%2F990\" \r\n" );
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document.write( "Edwin
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