document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=9823>Question 9823</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the exact fraction value foe the number 0.123123123....... using series only. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #5293 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=5293\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> not sure what you mean \"by Series\". The only way i am aware is to do the following:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "look at the repeating part, which here is 123. We need one whole section in front of the decimal point, so we need to multiply by 1000...\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let    r =   0.123123123...<BR>\n" );
document.write( "so 1000r = 123.123123123...\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now subtract the first from the second, leaving 999r = 123\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so r = 123/999\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "jon<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );