document.write( "Question 1019496: Hi\r
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document.write( "can you please show how to express this recurring decimal as a fraction\r
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document.write( "0.6898989898 etc\r
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document.write( "thanks \n" );
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Algebra.Com's Answer #635444 by Edwin McCravy(20056)![]() ![]() You can put this solution on YOUR website! 0.6898989898 \n" ); document.write( " \r\n" ); document.write( "Let the fraction be x. Then\r\n" ); document.write( "\r\n" ); document.write( "x = 0.6898989898\r\n" ); document.write( "\r\n" ); 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" ); document.write( "\r\n" ); document.write( "100x = 68.989898989\r\n" ); document.write( "\r\n" ); document.write( "Now put the original equation underneath that,\r\n" ); document.write( "lining up the decimal points\r\n" ); document.write( "\r\n" ); document.write( "100x = 68.98989898\r\n" ); document.write( " x = 0.6898989898\r\n" ); document.write( "--------------------\r\n" ); document.write( "\r\n" ); 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" ); document.write( "\r\n" ); document.write( "100x = 68.9898989898\r\n" ); document.write( " x = 0.6898989898\r\n" ); document.write( "--------------------\r\n" ); document.write( " 99x = 68.3000000000\r\n" ); document.write( "\r\n" ); document.write( " 99x = 68.3\r\n" ); document.write( "\r\n" ); document.write( "Now remove the decimal by multiplying both sides by 10\r\n" ); document.write( "\r\n" ); document.write( "990x = 683\r\n" ); document.write( "\r\n" ); document.write( " x =\r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |