document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=171887>Question 171887</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I arrived at a problem on my math homework on rational numbers that looked like this: (9.7...repeated.) I followed the steps that a previous tutor gave me, and i have been doing fine. I did N=9.7... and thenmultiplied each side by 10 and got 9N=?. 9.7x10=? I do not understand this concept whatsoever, please explain. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126981 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=126981\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=9.77777...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9.7777 ALIGN=MIDDLE  ALT=\"x=9.7777\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x=97.7777 ALIGN=MIDDLE  ALT=\"10x=97.7777\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 10. Notice how when we move the decimal one spot, the numbers after the decimal are EXACTLY the same as the numbers after the decimal above. \r<BR>\n" );
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document.write( "Why is this important? When we go to subtract 9.7777 from 97.7777, the numbers must match in order to completely cancel out the decimal portion.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x-x=97.7777-x ALIGN=MIDDLE  ALT=\"10x-x=97.7777-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now subtract \"x\" from both sides (since we did this to both sides, this does NOT change the equation)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x-x=97.7777-9.7777 ALIGN=MIDDLE  ALT=\"10x-x=97.7777-9.7777\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9.7777 ALIGN=MIDDLE  ALT=\"x=9.7777\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the original equation) on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x=88 ALIGN=MIDDLE  ALT=\"9x=88\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract. Notice how decimal portion of the numbers go away.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=88%2F9 ALIGN=MIDDLE  ALT=\"x=88%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 9 to isolate \"x\"\r<BR>\n" );
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document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=88%2F9 ALIGN=MIDDLE  ALT=\"x=88%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=88%2F9=9.77777 ALIGN=MIDDLE  ALT=\"88%2F9=9.77777\"   DISABLED_style= \"max-width:90%; height:auto;\" > (where the 7's repeat) </SPAN>\n" );
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