document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=356817>Question 356817</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My 4th grade son was given the equation 3x-9=70.  The answer the teacher wanted was x=26.33333 (with a line over the last three to show that it repeats indefinitely).  My question is:  how is this a valid equation?  When you plug the value of x back in, you are never going to get 70, but something that is slightly less than 70 (69.99999.....).  My son did get the answer she wanted, but it was my understanding that the whole point of finding the value of the variable was finding the value that makes the equation true. A second algebra teacher tells me that this is a completely valid question but couldn't explain why it is valid when it is untrue.  If someone could explain to me how 69.99999 = 70, I would be very grateful! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #254746 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=254746\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If someone could explain to me how 69.99999 = 70, I would be very grateful!<BR>\n" );
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document.write( "Let x = 69.999999 endlessly<BR>\n" );
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document.write( "Then 10x = 699.99999endlessly<BR>\n" );
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document.write( "Subtract the 1st equation from the 2nd to get:<BR>\n" );
document.write( "9x = 630<BR>\n" );
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document.write( "Divide by 9 to get:<BR>\n" );
document.write( "x = 70<BR>\n" );
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document.write( "Therefore x = 69.99999... = 70<BR>\n" );
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document.write( "Fact: Every repeating decimal can be written as a/b<BR>\n" );
document.write( "where a and b are integers and b is not zero.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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