document.write( "Question 102231: is seven an irrational number? \n" ); document.write( "
Algebra.Com's Answer #74292 by Edwin McCravy(20060) $\"\"$ $\"About$
You can put this solution on YOUR website!
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document.write( "Is seven an irrational number?\r\n" );
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document.write( "No for it is RATIOnal, because it is the RATIO of integers 7 to 1.\r\n" );
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document.write( "Any number is RATIOnal if it can be written \"an integer over an integer\"\r\n" );
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document.write( "These are rational numbers:\r\n" );
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document.write( ", , , , , \r\n" );
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document.write( "7.85674 is a rational number because we can begin by placing it over 1,\r\n" );
document.write( "like this  and then we can moving the decimal on top and \r\n" );
document.write( "bottom five places and we have  and that is \"an integer\r\n" );
document.write( "over an integer\". \r\n" );
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document.write( "An example of an irrational number is \r\n" );
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document.write( "2.67667666766667666667666666766666667666666667毽愧r\n" );
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document.write( "where after each 7 is one more 6 than was after the last 7 and this goes\r\n" );
document.write( "on forever.  It does not repeat the same block of digits forever, as\r\n" );
document.write( "each new block contains one more 6 than the last.\r\n" );
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document.write( "However a decimal such as\r\n" );
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document.write( "2.66776677667766776677667766776677毽愧r\n" );
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document.write( "is a RATONAL number because it repeats the block of digits 6677 forever.\r\n" );
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document.write( "Any termination decimal or non-terminating decimal WHICH REPEATS THE SAME\r\n" );
document.write( "block of digits forever can be shown to represent a rational number.\r\n" );
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document.write( "Incidentally, the never ending decimal above,\r\n" );
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document.write( "2.66776677667766776677667766776677毽愧r\n" );
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document.write( "is RATIONAL because it is equivalent to the fraction:\r\n" );
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document.write( " which is \"an integer over an integer\".\r\n" );
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document.write( "Don't believe it?  Watch this long division:\r\n" );
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document.write( "            2.667766\r\n" );
document.write( "     909)2425.000000\r\n" );
document.write( "         1818       \r\n" );
document.write( "          607 0    \r\n" );
document.write( "          545 4    \r\n" );
document.write( "           61 60   \r\n" );
document.write( "           54 54   \r\n" );
document.write( "            7 060   \r\n" );
document.write( "            6 363  \r\n" );
document.write( "              6970  \r\n" );
document.write( "              6363 \r\n" );
document.write( "               6070\r\n" );
document.write( "               5454\r\n" );
document.write( "                6160    \r\n" );
document.write( "                5454\r\n" );
document.write( "                 706\r\n" );
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document.write( "Look at the division and you can see that you\r\n" );
document.write( "will keep getting the same block of digits \r\n" );
document.write( "6677 forever.\r\n" );
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document.write( "Rational numbers are numbers that can be written\r\n" );
document.write( "as COMMON FRACTIONS, either proper of improper.\r\n" );
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document.write( "Irrational number are those which can't be so\r\n" );
document.write( "written.\r\n" );
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document.write( " is an irrational number. It starts off:\r\n" );
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document.write( "1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641572735013846230912297024924836055850737212644121497099935831432226659275055927557999505011527820605714701095599716059702745345968620147285... \r\n" );
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document.write( "It never stops and it never repeats the same set of digits over and over\r\n" );
document.write( "forever.  Check this website and see it carried to a million decimal\r\n" );
document.write( "places.  \r\n" );
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document.write( "http://antwrp.gsfc.nasa.gov/htmltest/gifcity/sqrt2.1mil\r\n" );
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document.write( " is another irrational number.  It starts off:\r\n" );
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document.write( "3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609...\r\n" );
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document.write( "It never stops and it never repeats the same set of digits over and over\r\n" );
document.write( "forever.  Check out this website:   \r\n" );
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document.write( "http://pi.ytmnd.com/\r\n" );
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document.write( "and hear a bunch of the digits of pi sung.\r\n" );
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document.write( "Edwin
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