document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=632433>Question 632433</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find an irratational number between .757575... and .767676... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #398388 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5397)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=398388\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The number 0.757575... is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75%2F99 ALIGN=MIDDLE  ALT=\"75%2F99\"   DISABLED_style= \"max-width:90%; height:auto;\" > and 0.767676... is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=76%2F99 ALIGN=MIDDLE  ALT=\"76%2F99\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "You can figure out 0.757575... as a fraction because<BR>\n" );
document.write( "if n=0.757575... , then 100n=75.757575... and subtracting one equation from the other, you get<BR>\n" );
document.write( "100n-n=75 --> (100-1)n=75 --> 99n=75 --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=75%2F99 ALIGN=MIDDLE  ALT=\"n=75%2F99\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can figure out that 0.767676... = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=76%2F99 ALIGN=MIDDLE  ALT=\"76%2F99\"   DISABLED_style= \"max-width:90%; height:auto;\" > similarly.<BR>\n" );
document.write( "You can choose an integer m between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75%5E2=5625 ALIGN=MIDDLE  ALT=\"75%5E2=5625\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=76%5E2=5776 ALIGN=MIDDLE  ALT=\"76%5E2=5776\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2625%3Cm%3C5776 ALIGN=MIDDLE  ALT=\"2625%3Cm%3C5776\"   DISABLED_style= \"max-width:90%; height:auto;\" >),<BR>\n" );
document.write( "and then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28m%29%2F99 ALIGN=MIDDLE  ALT=\"sqrt%28m%29%2F99\"   DISABLED_style= \"max-width:90%; height:auto;\" > will be an irrational number between 0.757575... and 0.767676... because\r<BR>\n" );
document.write( "\n" );
document.write( "0.757575... = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75%2F99=sqrt%285625%29%2F99%3Csqrt%28m%29%2F99%3Csqrt%285776%29%2F99=76%2F99 ALIGN=MIDDLE  ALT=\"75%2F99=sqrt%285625%29%2F99%3Csqrt%28m%29%2F99%3Csqrt%285776%29%2F99=76%2F99\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.767676...\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );