document.write( "Question 355106: Could you please give me an example of a real number,that is not an irrational number? \n" ); document.write( "
Algebra.Com's Answer #253635 by Edwin McCravy(20054) $\"\"$ $\"About$
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document.write( " is a real number, and it is not irrational, it is RATIOnal because it\r\n" );
document.write( "is the RATIO of two integers, 1 and 2.   \r\n" );
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document.write( " and  are irrational numbers because they cannot be\r\n" );
document.write( "expressed as the ratio of two integers.\r\n" );
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document.write( "Notice that the first five letters of the word \"rational\" is \"ratio\".  And\r\n" );
document.write( "that means \"the ratio of two integers\".\r\n" );
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document.write( "In fact integers themselves are rational.  For instance the integer \r\n" );
document.write( "is rational because it can be expressed as the ratio of two integers  or even as .\r\n" );
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document.write( "Repeating decimals are rational because they can be expressed as a ratio\r\n" );
document.write( "of two integers.\r\n" );
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document.write( ".639639639639639.....\r\n" );
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document.write( "is a rational number because it doesn't have to be expressed as that decimal\r\n" );
document.write( "that repeats forever, for it can be expressed instead as  as\r\n" );
document.write( "you can see from the following long division:\r\n" );
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document.write( "      .639639639.......\r\n" );
document.write( "111)71.000000000.......\r\n" );
document.write( "    66 6\r\n" );
document.write( "     4 40\r\n" );
document.write( "     3 33\r\n" );
document.write( "     1 070\r\n" );
document.write( "       999\r\n" );
document.write( "        710\r\n" );
document.write( "        666\r\n" );
document.write( "         440   \r\n" );
document.write( "         333 \r\n" );
document.write( "         1070\r\n" );
document.write( "          999\r\n" );
document.write( "           710\r\n" );
document.write( "           666\r\n" );
document.write( "            440\r\n" );
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document.write( "etc. etc. etc.  \r\n" );
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document.write( "However this decimal\r\n" );
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document.write( ".232332333233332333332...\r\n" );
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document.write( "although it has a pattern, it in irrational because it is impossible\r\n" );
document.write( "to find to integers that it is the ratio as we could above with \r\n" );
document.write( ".639639639639639.....\r\n" );
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document.write( " is often believed to be the rational number  but\r\n" );
document.write( "22/7 is 3.142857142857142857....\r\n" );
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document.write( "and it keeps repeating that block of digits \"142857\" over and over\r\n" );
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document.write( "whereas the first digits of  are 3.1415926535898...\r\n" );
document.write( "and it never repeats a block of digits.\r\n" );
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document.write( "So  is only close to . It isn't  at all.\r\n" );
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document.write( " is rational but  is irrational.\r\n" );
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document.write( "Edwin
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