document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=996939>Question 996939</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Is \"-2\" a rational or irrational number and how because i am struggling with what is a rational or irrational number  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #615197 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=615197\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Numbers that may first be developed were first used for counting whole, entire things, so they were 1, 2, 3, 4, 5, and all of what result when ADD ONE is tried,... without end.  These are NATURAL Numbers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A count of No Things was given a number, Zero, which we learned to symbolize with the numeral, 0.  The numbers  starting at zero and incremented by ADD ONE are 0, 1, 2, 3, 4, 5, 6, 7, ... and on and on.  These are the WHOLE Numbers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We can put these whole numbers on a line and call this \"the number line\".  People learned to right starting from 0 on the number line, and labeling numbers on the line going to the right as one direction; and going in the opposite direction (FROM Zero) as NEGATIVE numbers, but now we have numbers which go like this:<BR>\n" );
document.write( "..., -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4,...<BR>\n" );
document.write( "and the numbers to the left of zero on this line are the NEGATIVE whole numbers while the numbers to the right of zero are the POSITIVE whole numbers.<BR>\n" );
document.write( "These numbers are all INTEGERS.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Another kind of number was found that can be expressed as the RATIO of two integers.  Some of these ratios are BETWEEN integers and some are the same as an integer.<BR>\n" );
document.write( "-<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5 ALIGN=MIDDLE  ALT=\"2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is such a ratio of two integers.  Try to check where this goes on a number line; and find that it fits someplace between 0 and 1.  Notice that because it is between two integers, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5 ALIGN=MIDDLE  ALT=\"2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is NOT an integer.  But, it is a rational number.  Another example,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is ratio of two integers, but it fits between two integers.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not an integers, but it is a RATIONAL number.<BR>\n" );
document.write( "-<BR>\n" );
document.write( "These numbers which can be expressed as the ratio of two integers make up the RATIONAL Numbers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "YOUR example of  \"-2\" is two types of numbers.<BR>\n" );
document.write( "It is an integer, obviously because it is a member of the integers, and you see that is is the exact size of one of the whole numbers  ( the whole number 2) but is negative; so it is a member of the set of integers.  <BR>\n" );
document.write( "... It is also a rational number because you can express -2 as   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F1 ALIGN=MIDDLE  ALT=\"-2%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or as  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28-1%29 ALIGN=MIDDLE  ALT=\"2%2F%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You also asked, is  -2 an irrational number? <BR>\n" );
document.write( "NO.  -2 is RATIONAL and also an INTEGER.  An irrational number CANNOT be expressed as the ratio of two integers. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );