document.write( "Question 75572This question is from textbook algebra
\n" ); document.write( ": write the decimal expansions for these rational number. tell whether the expansions are terminating or repeating.\r
\n" ); document.write( "\n" ); document.write( "Find the rational number equivalents for these decimal expansions.\r
\n" ); document.write( "\n" ); document.write( "tell whether they are rational or irrational\r
\n" ); document.write( "\n" ); document.write( "simplify the following radicals. be sure to check your answers\r
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Algebra.Com's Answer #54243 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
You didn't give any problems,\r\n" );
document.write( "so I'll make some up. I hope they are\r\n" );
document.write( "like the ones you were asked to solve.\r\n" );
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document.write( "All rational numbers expressed\r\n" );
document.write( "as decimals will either terminate\r\n" );
document.write( "or repeat a block of digits\r\n" );
document.write( "forever.  That's because in long\r\n" );
document.write( "division all the remainders will\r\n" );
document.write( "always be less than the divisor,\r\n" );
document.write( "so sooner or later the remainder\r\n" );
document.write( "will either be 0 or will be the\r\n" );
document.write( "repeat of a remainder obtained\r\n" );
document.write( "earlier.\r\n" );
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document.write( "write the decimal expansions for these \r\n" );
document.write( "rational numbers. tell whether the \r\n" );
document.write( "expansions are terminating or repeating. \r\n" );
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document.write( "#1.   9/32\r\n" );
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document.write( "Use long division:\r\n" );
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document.write( "    .28125 \r\n" );
document.write( "32)9.00000\r\n" );
document.write( "   6 4\r\n" );
document.write( "   2 60\r\n" );
document.write( "   2 56\r\n" );
document.write( "      40\r\n" );
document.write( "      32\r\n" );
document.write( "       80\r\n" );
document.write( "       64\r\n" );
document.write( "       160\r\n" );
document.write( "       160\r\n" );
document.write( "         0\r\n" );
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document.write( "Terminating because the division \r\n" );
document.write( "eventually has 0 remainder\r\n" );
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document.write( "#2. 15/22\r\n" );
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document.write( "Again use long division:\r\n" );
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document.write( "     .6818 \r\n" );
document.write( "22)15.0000 \r\n" );
document.write( "   13 2\r\n" );
document.write( "    1 80\r\n" );
document.write( "    1 76\r\n" );
document.write( "       40\r\n" );
document.write( "       22\r\n" );
document.write( "       18 \r\n" );
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document.write( "This is a repeating decimal because the same \r\n" );
document.write( "non-zero remainder 18 occurred twice in the \r\n" );
document.write( "long division. These two 18's are indicated in \r\n" );
document.write( "red above.\r\n" );
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document.write( "--------------------------------------------\r\n" );
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document.write( "Find the rational number equivalents for these \r\n" );
document.write( "decimal expansions. tell whether they are \r\n" );
document.write( "rational or irrational\r\n" );
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document.write( "#3.   .185185185185···\r\n" );
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document.write( "Let N = .185185185185···\r\n" );
document.write( "There are 3 digits in the repeating block\r\n" );
document.write( "\"185\", so multiply by 103 or\r\n" );
document.write( "1000\r\n" );
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document.write( "1000N = 185.185185185···\r\n" );
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document.write( "Now place the first equation underneath\r\n" );
document.write( "and subtract the two equations\r\n" );
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document.write( "1000N = 185.185185185···\r\n" );
document.write( "    N =    .185185185185···\r\n" );
document.write( " 999N = 185.000000000\r\n" );
document.write( " 999N = 185\r\n" );
document.write( "    N = 185/999\r\n" );
document.write( "that reduces to\r\n" );
document.write( "    N = 5/27\r\n" );
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document.write( "This is RATIOnal because it is the\r\n" );
document.write( "RATIO of two integers\r\n" );
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document.write( "#2.  2.9373737837···\r\n" );
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document.write( "Let N = 2.937373737··· \r\n" );
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document.write( "There are 2 digits in the repeating block\r\n" );
document.write( "\"37\", so multiply by 102 or\r\n" );
document.write( "100\r\n" );
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document.write( "100N = 293.737373737···\r\n" );
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document.write( "Now place the first equation underneath\r\n" );
document.write( "and subtract the two equations\r\n" );
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document.write( "100N = 293.737373737···\r\n" );
document.write( "   N =   2.93737373737···\r\n" );
document.write( " 99N = 290.800000000···\r\n" );
document.write( " 99N = 290.8\r\n" );
document.write( "Clear of decimals by multiplying thru\r\n" );
document.write( "by 10\r\n" );
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document.write( "990N = 2908\r\n" );
document.write( "   N = 2908/990\r\n" );
document.write( "that reduces to\r\n" );
document.write( "    N = 1454/495\r\n" );
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document.write( "This is RATIOnal because it is the\r\n" );
document.write( "RATIO of two integers\r\n" );
document.write( "  \r\n" );
document.write( "#3.  .72772277722277772222···\r\n" );
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document.write( "This is IRRATIONAL because  \r\n" );
document.write( "there is no block of repeating\r\n" );
document.write( "digits.\r\n" );
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document.write( "--------------------------------------------\r\n" );
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document.write( "simplify the following \r\n" );
document.write( "radicals. \r\n" );
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document.write( "#4.  \"sqrt%28252%29+=+sqrt%2836%2A7%29+=+sqrt%2836%29sqrt%287%29+=+6sqrt%287%29\"\r\n" );
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document.write( "#5. \r\n" );
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document.write( "Edwin

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