document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=894634>Question 894634</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Express 0.312 in base 10 as a binary number.<BR>\n" );
document.write( "2.)convert the following in base ten to decimal<BR>\n" );
document.write( "a.) (57/64)ten </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #542216 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=542216\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .312 = 312/1000\r<BR>\n" );
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document.write( "312 = 100111000 in binary.<BR>\n" );
document.write( "1000 = 1111101000\r<BR>\n" );
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document.write( ".312 = 312/1000 = 100111000 / 1111101000\r<BR>\n" );
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document.write( "dividing in binary, you get:\r<BR>\n" );
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document.write( "100111000 ÷ 11111010 = 1.001111110111110011\r<BR>\n" );
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document.write( "i did not do this by hand.\r<BR>\n" );
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document.write( "i used a binary calculator.\r<BR>\n" );
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document.write( "the process is not very complex but very cumbersome and highly prone to errors and is not recommended to attempt by hand for anything but the simplest numbers.\r<BR>\n" );
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document.write( "i'll try a simpler number that should show you that the process is correct.\r<BR>\n" );
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document.write( ".25 = 25/100 = 11001 / 1100100\r<BR>\n" );
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document.write( "we'll use the calculator again to get:\r<BR>\n" );
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document.write( "11001 ÷ 1100100 = 0.01\r<BR>\n" );
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document.write( ".01 in binary is 0 / 2^1 + 1 / 2^2 which is equal to 0 + 1/4 which is equal to 1/4 which is equal to .25\r<BR>\n" );
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document.write( "binary number go like this:\r<BR>\n" );
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document.write( "going left from the decimal point, you have:\r<BR>\n" );
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document.write( "2^0<BR>\n" );
document.write( "2^1<BR>\n" );
document.write( "2^2<BR>\n" );
document.write( "2^3<BR>\n" );
document.write( "2^4<BR>\n" );
document.write( "....\r<BR>\n" );
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document.write( "going right from the decimal point you have:\r<BR>\n" );
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document.write( "1/2^1<BR>\n" );
document.write( "1/2^2<BR>\n" );
document.write( "1/2^3<BR>\n" );
document.write( "1/2^4<BR>\n" );
document.write( "....\r<BR>\n" );
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document.write( "the binary division calculator can be found at:\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.miniwebtool.com/binary-calculator/?number1=11001&operate=4&number2=1100100\" target = \"_blank\">http://www.miniwebtool.com/binary-calculator/?number1=11001&operate=4&number2=1100100</a>\r<BR>\n" );
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document.write( "if you want to learn how to do the calculations manually, then there's some links that will show you how to do it.\r<BR>\n" );
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document.write( "some of them are:\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://academic.evergreen.edu/projects/biophysics/technotes/misc/bin_math.htm\" target = \"_blank\">http://academic.evergreen.edu/projects/biophysics/technotes/misc/bin_math.htm</a><BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.exploringbinary.com/binary-division/\" target = \"_blank\">http://www.exploringbinary.com/binary-division/</a><BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.binarymath.info/multiplication-division.php\" target = \"_blank\">http://www.binarymath.info/multiplication-division.php</a>\r<BR>\n" );
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document.write( "it is obvious that the number you asked for in binary was very complicated and certainly not desirable to perform by hand.\r<BR>\n" );
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document.write( "the calculator came in quite handy for that even though we had to convert .312 into 312 / 1000 and then convert that to binary to get 100111000 / 1111101000 and then plugging that into the calculator.\r<BR>\n" );
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document.write( "the second part of your question appears to be easier.\r<BR>\n" );
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document.write( "i used my calculator to get 57/64 = .890625\r<BR>\n" );
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document.write( "that could also have been done by hand in a similar manner that the binary division is done by hand, but why go through all that if you don't have to?\r<BR>\n" );
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document.write( "bottom line is that binary division is not much different then decimal division.\r<BR>\n" );
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document.write( "the process if the same, but the base of the number system you are dealing with is different and you have to account for that.\r<BR>\n" );
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document.write( "i couldn't find a reference that talked about converting directly from decimal to binary when the decimal number was a fraction that was converted to a decimal.\r<BR>\n" );
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document.write( "perhaps there's a way.\r<BR>\n" );
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document.write( "i just couldn't find it.<BR>\n" );
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