document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=344951>Question 344951</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. x=1.9285714285714285714.....<BR>\n" );
document.write( "   y=0.3333333333333333333......<BR>\n" );
document.write( "   Evaluate x+y<BR>\n" );
document.write( "2. A system with two inputs of periodic infinite decimal numbers is designed such that,it performs addition between two inputs and gives single output. Would the output be a periodic decimal number? Discuss the answer using mathematical analysis of the situation.<BR>\n" );
document.write( "3. If you are required to use such a single system and form a 6 input:1 output<BR>\n" );
document.write( "system will you be able to guarantee that the output would be same as you discussed in be? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #246811 by </B><A HREF=/tutors/aboutme.mpl?userid=Jk22><B>Jk22(389)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Jk22><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=Jk22><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=246811\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. x=1.9285714285714285714.....<BR>\n" );
document.write( "   y=0.3333333333333333333......<BR>\n" );
document.write( "   Evaluate x+y<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Either we notice that 428571 is typical of seventh fraction : x=10/7+0.5 <BR>\n" );
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document.write( "x+y=1/3+10/7+1/2=(14+60+21)/42=95/42<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "or by using : 0.a1a2a3...an(periodic)=a1a2a3...an/99...9 denominator : n 9's))<BR>\n" );
document.write( "  <BR>\n" );
document.write( "y=3/9=1/3, x=1.9+0.0285714...=19/10+1/10*285714/999999<BR>\n" );
document.write( "  <BR>\n" );
document.write( "x+y=1/3+19/10+285714/9999990=(3333330+19*999999+285714)/9999990<BR>\n" );
document.write( "=(3619044+19000000-19)/9999990=(22619044-19)/9999990=22619025/9999990 (simpl 5)<BR>\n" );
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document.write( "=4523805/1999998 (simpl 3)=1507935/666666(simpl 3) =502645/222222(simpl 11) <BR>\n" );
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document.write( "=45695/20202(simpl 13)=3515/1554(simpl 37)=95/42<BR>\n" );
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document.write( "2. and 3. since a periodic decimal number can be written in form of a fraction with the formula above, the sum of periodic decimal number will be a fraction again, which is a periodic decimal number. </SPAN>\n" );
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