document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=391682>Question 391682</A>: <I><SPAN STYLE=\"word-break: break-all;\">                                                                  _   <BR>\n" );
document.write( "Express the (repeating) decimal 1.9 as a quotient of two integers. *NOTE it has to be set up something like this:<BR>\n" );
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document.write( "n = 1.9<BR>\n" );
document.write( "the answer is the fraction (2/1) but I do not know how this is. Please Help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #278058 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=278058\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The number you're referring to is 1.99999....there are probably a dozen ways to prove this is equal to 2.\r<BR>\n" );
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document.write( "We could consider the infinite series <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%289%2A10%5E%28-k%29%2C+k+=+1%2C+infinity%29+=+9%2F10+%2B+9%2F100+%2B+9%2F1000 ALIGN=MIDDLE  ALT=\"sum%289%2A10%5E%28-k%29%2C+k+=+1%2C+infinity%29+=+9%2F10+%2B+9%2F100+%2B+9%2F1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > + ...If you know that the sum of the terms of a convergent geometric sequence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ar%5Ei ALIGN=MIDDLE  ALT=\"ar%5Ei\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F%28r-1%29 ALIGN=MIDDLE  ALT=\"a%2F%28r-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can replace a = 9, and r = 10 to get 9/9 or 1. Finally, add 1 (since the number is 1.9999 instead of .9999) to get 2.\r<BR>\n" );
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document.write( "Another possible way works like this:\r<BR>\n" );
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document.write( "1/9 = .11111....<BR>\n" );
document.write( "9/9 = 9(.11111....) = .99999....\r<BR>\n" );
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document.write( "However 9/9 = 1 so .99999.... = 1, and 1.99999.... = 2 = 2/1. </SPAN>\n" );
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