document.write( "Question 1188231: Express the nonterminating repeating decimal 2.045045045... as a fraction. \n" ); document.write( "
Algebra.Com's Answer #819254 by mccravyedwin(407)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Since you posted this in the Sequences-and-series section, maybe you wanted to\r\n" );
document.write( "see it done as an infinite geometric series:\r\n" );
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document.write( "2 + .045\r\n" );
document.write( "  + .000045\r\n" );
document.write( "  + .000000045\r\n" );
document.write( "  + ...........\r\n" );
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document.write( "2 + 0.045 + 0.000045 + 0.000000045 + ...\r\n" );
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document.write( "2 + 4.5x10-2 + 4.5x10-5 + 4.5x10-8 + ...\r\n" );
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document.write( "The terms to the right of 2 form an infinite geometric series with first term =\r\n" );
document.write( "a1 = 4.5x10-2 and common ratio r = 10-3\r\n" );
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document.write( "\"S%5Binfinity%5D\"\"%22%22=%22%22\"\"a%5B1%5D%2F%281-r%29%5B%22%22%5D\"\r\n" );
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document.write( "\"S%5Binfinity%5D\"\"%22%22=%22%22\"\"%284.5%2A10%5E%28-2%29%29%2F%281-10%5E%28-3%29%29%5B%22%22%5D\"\r\n" );
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document.write( "Multiply numerator and denominator by 103\r\n" );
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document.write( "\"S%5Binfinity%5D\"\"%22%22=%22%22\"\"%22%22=%22%22\"\"%284.5%2A10%5E1%29%2F%2810%5E3-10%5E0%29\"\"%22%22=%22%22\"\"45%2F%281000-1%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "\"45%2F999\"\"%22%22=%22%22\"\"5%2F111\"\r\n" );
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document.write( "So the fraction is \"2%265%2F111\" or \"227%2F11\"\r\n" );
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document.write( "Edwin
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