document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=178091>Question 178091</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is irrational numbers and what is rational numbers?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #133094 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=133094\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a rational number is a number that you can make a ratio out of with an integer on top and an integer on the bottom.<BR>\n" );
document.write( "1/2 is a rational number.<BR>\n" );
document.write( "3/4 is rational.<BR>\n" );
document.write( "7/9 is rational.<BR>\n" );
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document.write( "an irrational number is a number that you cannot make a ratio out of using integers on the top and integers on the bottom.<BR>\n" );
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document.write( "a rational number can be never ending when you take the decimal equivalent.<BR>\n" );
document.write( "2/3 would be an example:<BR>\n" );
document.write( "2/3 = .6666666666666666666666666666666666666666666666666..........<BR>\n" );
document.write( "while the decimal is never ending, it is still a rational number because it is the result of a ratio of two integers.<BR>\n" );
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document.write( "if you see a never ending decimal, and you see a recognizable pattern, then the number is most likely a rational number.<BR>\n" );
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document.write( "if you see a never ending decimal, but you cannot see a recognizable pattern, then the number is most likely an irrational number.<BR>\n" );
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document.write( "from the web:<BR>\n" );
document.write( "Definition: A rational number is a number that can be represented as a fraction m/n, where m and n are integers, and n is not equal to 0.<BR>\n" );
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document.write( "one website said pi was a rational number.<BR>\n" );
document.write( "another said it wasn't.<BR>\n" );
document.write( "i agree with the one that said it wasn't because the decimal goes on and on and there is no recognizable pattern to the digits.<BR>\n" );
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document.write( "square root of 4 is a rational number because the answer is 2 and any integer is a rational number since it can be expressed as the ratio of 2/1.<BR>\n" );
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document.write( "the square root of 3 is not a rational number.<BR>\n" );
document.write( "take the square root of 3.<BR>\n" );
document.write( "the decimal equivalent of that is:<BR>\n" );
document.write( "1.732050807568880000000000000000<BR>\n" );
document.write( "this number goes on and on but there is no recognizable pattern to the digits.<BR>\n" );
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document.write( "take 1/7.<BR>\n" );
document.write( "the decimal equivalent of that is:<BR>\n" );
document.write( "0.142857142857143000000000000000<BR>\n" );
document.write( "while this number goes on and on, there is a recognizable pattern to the digits.<BR>\n" );
document.write( "142857 then 142857 then 143000 which is probably 142857 but the software package i used (microsoft excel) stopped after so many significant digits and then rounded.<BR>\n" );
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document.write( "pi is not a rational number.<BR>\n" );
document.write( "this is the microsoft excel representation of pi up to 15 significant digits.<BR>\n" );
document.write( "3.141592653589790000000000000000<BR>\n" );
document.write( "as you can see, there is no recognizable pattern to the digits.<BR>\n" );
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document.write( "the strict definition is as stated above (m/n when m and n are integers and n not equal to 0).<BR>\n" );
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document.write( "recognizing a decimal equivalent as a rational number is a little more difficult because most calculators and even software programs don't go out far enough to let you see a pattern if there is one.  if the pattern shows up early you're home free.  if the decimal equivalent is not never ending, i.e. it is a discrete number of digits, then the number for sure a rational number.<BR>\n" );
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document.write( "take .643105<BR>\n" );
document.write( "this number has a finite number of digits and can be expressed as 643105/1000000<BR>\n" );
document.write( "which are both integers.<BR>\n" );
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