document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1108765>Question 1108765</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Express 1.234 (with the 34 recurring) as a fraction in simplest form. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #723772 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=723772\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Ignore the whole number part and convert the repeating decimal; then add the whole number part back into the answer.<br><BR>\n" );
document.write( "Slow, formal algebraic method....<br><BR>\n" );
document.write( "Call the number x.  Then, since 2 digits are repeating, multiply x by 100 and subtract x from the result.  The repeating digits will line up and are cancelled by the subtraction.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100x+=+23.4343434 ALIGN=MIDDLE  ALT=\"100x+=+23.4343434\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+.2343434 ALIGN=MIDDLE  ALT=\"x+=+.2343434\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=99x+=+23.2 ALIGN=MIDDLE  ALT=\"99x+=+23.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=990x+=+232 ALIGN=MIDDLE  ALT=\"990x+=+232\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+232%2F990+=+116%2F495 ALIGN=MIDDLE  ALT=\"x+=+232%2F990+=+116%2F495\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then the final answer is the mixed number 1 116/495; or, if an improper fraction answer is asked for, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28495%2B116%29%2F495+=+611%2F495 ALIGN=MIDDLE  ALT=\"%28495%2B116%29%2F495+=+611%2F495\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "Shortcut....<br><BR>\n" );
document.write( "Write out on paper the process shown above to see how this shortcut works....<br><BR>\n" );
document.write( "The denominator of the fraction in unsimplified form is 990, because there are two digits that repeat and one digit that does not repeat.  In general, the denominator is one 9 for each repeating digit followed by one 0 for each non-repeating digit.<br><BR>\n" );
document.write( "The numerator of the fraction is (the non-repeating digits plus one cycle of the repeating digits) minus (the non-repeating digits) -- in your example, \"234 - 2\".<br><BR>\n" );
document.write( "So without going through all the formal algebra shown earlier, you can just write down the (unsimplified) answer:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28234-2%29%2F990+=+232%2F990 ALIGN=MIDDLE  ALT=\"%28234-2%29%2F990+=+232%2F990\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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