document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=750467>Question 750467</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me\r<BR>\n" );
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document.write( "Find the fractions equal to the given decimals\r<BR>\n" );
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document.write( "1. 0.82222... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #456591 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=456591\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Change to a rational number the given number:<BR>\n" );
document.write( "(1) n = 0.8222...<BR>\n" );
document.write( "First we \"fix\" the decimal to be a whole number plus a repeating decimal. In this case<BR>\n" );
document.write( "(2) n = 8.222.../10 or<BR>\n" );
document.write( "(3) n = (8 + .222...)/10<BR>\n" );
document.write( "We know that a single digit m divided by 9 is<BR>\n" );
document.write( "(4) m/9 = 0.mmm... or .m repeated<BR>\n" );
document.write( "In the given case in (3) we have<BR>\n" );
document.write( "(5) 0.222.... which by applying (4) becomes<BR>\n" );
document.write( "(6) 2/9 = 0.222...<BR>\n" );
document.write( "Now place the identity of (6) into (3) and get<BR>\n" );
document.write( "(7) n = (8 + 2/9)/10<BR>\n" );
document.write( "Now simplify (7) to get<BR>\n" );
document.write( "(8) n = ((72+2)/9)/10 or<BR>\n" );
document.write( "(9) n = (74/9)/10 or<BR>\n" );
document.write( "(10) n = 74/90 or<BR>\n" );
document.write( "(11) n = 37/45<BR>\n" );
document.write( "To ckeck the answer do the following<BR>\n" );
document.write( "Is (0.8222.. = 37/45)?<BR>\n" );
document.write( "Is (0.8222.. = 74/90)?<BR>\n" );
document.write( "Is (90*0.8222...) = 74)?<BR>\n" );
document.write( "Is (9*8.222... = 74)?<BR>\n" );
document.write( "Is (72 + 9*0.222... = 74)?<BR>\n" );
document.write( "Is (72 + 9*2/9 = 74)?<BR>\n" );
document.write( "Is (72 + 2 = 74)?<BR>\n" );
document.write( "Is (74 = 74)? Yes<BR>\n" );
document.write( "Answer: 37/45 is the rational number equivalent of the decimal 0.8222...<BR>\n" );
document.write( "Hint: If you have a two digit repeating number, such as<BR>\n" );
document.write( "(12) 0.ababab.... it is the rational number<BR>\n" );
document.write( "(13) ab/99 and if you have a three digit repeating number, such as<BR>\n" );
document.write( "(14) 0.abcabcabc... it is the rational number<BR>\n" );
document.write( "(15) abc/999 and four<BR>\n" );
document.write( "(16) abcd/9999 etc.<BR>\n" );
document.write( "PS You can do all of the above on a calculator.\r<BR>\n" );
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