document.write( "Question 1107628: In the decimal expansion of the rational number 2/13 what is the 200th digit to the right of the decimal point?
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Algebra.Com's Answer #722643 by AnlytcPhil(1807)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "   0.153846... \r\n" );
document.write( "13)2.000000...\r\n" );
document.write( "   1 3\r\n" );
document.write( "     70\r\n" );
document.write( "     65\r\n" );
document.write( "      50\r\n" );
document.write( "      39\r\n" );
document.write( "      110\r\n" );
document.write( "      104\r\n" );
document.write( "        60\r\n" );
document.write( "        52\r\n" );
document.write( "         80\r\n" );
document.write( "         78\r\n" );
document.write( "          2  <--starts repeating block of 6 digits 153846\r\n" );
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document.write( "200/6 = 33 1/3\r\n" );
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document.write( "So the decimal will have gone through exactly 33 complete \r\n" );
document.write( "blocks of 6 digits each on the 33×6 = 198th digits so the \r\n" );
document.write( "199th digit will be the start of a new block and will be 1.\r\n" );
document.write( "Then the 200th digit will be 5.\r\n" );
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document.write( "Or you can simply say 200 mod 6 = 2, so the 200th digit is\r\n" );
document.write( "the same as the 2nd digit, or 5\r\n" );
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document.write( "Answer: c) 5\r\n" );
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document.write( "[It has been shown statistically using multiple-choice tests\r\n" );
document.write( "and exams that the probability is always higher that the correct\r\n" );
document.write( "answer is choice c).  So any time you must guess, always\r\n" );
document.write( "guess c).   :)  ]\r\n" );
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document.write( "Edwin
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