document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=94772>Question 94772</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Convert 12kg/ml into grams/liter </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #69007 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=69007\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+kg%2Fml ALIGN=MIDDLE  ALT=\"12+kg%2Fml\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To convert this to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=gms%2Fltr ALIGN=MIDDLE  ALT=\"gms%2Fltr\"   DISABLED_style= \"max-width:90%; height:auto;\" > we need to recall that:<BR>\n" );
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document.write( "1 kg = 1000 gms<BR>\n" );
document.write( "and<BR>\n" );
document.write( "1 ltr = 1000 mls<BR>\n" );
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document.write( "We are going to multiply the original amount we were give by two conversions, one conversion<BR>\n" );
document.write( "that changes kg to gms and one that changes ml to ltrs.  So we have to have our conversions<BR>\n" );
document.write( "arranged so that the kg in the conversion will cancel the kg in the problem we were given<BR>\n" );
document.write( "and the ml in the conversion will also cancel the ml in the problem we were given.<BR>\n" );
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document.write( "To cancel the kg in the given problem (which is in the numerator) we need a kg in the <BR>\n" );
document.write( "denominator. So our conversion factor will have kg in the denominator and gms in the numerator.<BR>\n" );
document.write( "So the weight conversion must be:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281000+gms%29%2F%281kg%29%29 ALIGN=MIDDLE  ALT=\"%28%281000+gms%29%2F%281kg%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To cancel the ml in the given problem (which is in the denominator) we need a ml in the numerator.<BR>\n" );
document.write( "So our conversion factor will have ml in the numerator and ltr in the denominator. <BR>\n" );
document.write( "That means that this conversion factor for the liquid measure must be:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281000mls%29%2F%281+ltr%29%29 ALIGN=MIDDLE  ALT=\"%28%281000mls%29%2F%281+ltr%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now all that we need to do is to multiply the original given by these two conversion<BR>\n" );
document.write( "factors as follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2812kg%29%2F%28ml%29%29%2A%28%281000+gms%29%2F%281kg%29%29%2A%28%281000mls%29%2F%281+ltr%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice how the weight units cancel:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2A%28cross%28kg%29%29%2F%28ml%29%29%2A%28%281000+gms%29%2F%281%2Across%28kg%29%29%29%2A%28%281000mls%29%2F%281+ltr%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next notice how the liquid measure units also cancel:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2A%28cross%28kg%29%29%2F%28cross%28ml%29%29%29%2A%28%281000+gms%29%2F%281%2Across%28kg%29%29%29%2A%28%281000%2Across%28mls%29%29%2F%281+ltr%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then notice that in the denominators we can ignore the \"1\" associated with the kg and with<BR>\n" );
document.write( "the ltr.<BR>\n" );
document.write( "As a result we are left with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2A%28cross%28kg%29%29%2F%28cross%28ml%29%29%29%2A%28%281000+gms%29%2F%28cross%28kg%29%29%29%2A%28%281000%2Across%28mls%29%29%2F%28+ltr%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can now see that the remaining units are gms in the numerator and ltr in the denominator,<BR>\n" );
document.write( "just as the problem asked for. All you have to do is multiply the numbers that all appear<BR>\n" );
document.write( "in the numerator<BR>\n" );
document.write( "to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2A1000%2A1000%29gm%2Fltr+=+12000000+%28gm%2Fltr%29+ ALIGN=MIDDLE  ALT=\"%2812%2A1000%2A1000%29gm%2Fltr+=+12000000+%28gm%2Fltr%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To shorten this you can write the answer in the form of exponential notation as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2A10%5E%286%29+%28gm%2Fltr%29 ALIGN=MIDDLE  ALT=\"12%2A10%5E%286%29+%28gm%2Fltr%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "or in scientific notation as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.2%2A10%5E%287%29+%28gm%2Fltr%29 ALIGN=MIDDLE  ALT=\"1.2%2A10%5E%287%29+%28gm%2Fltr%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Once you get the hang of this process, it will go much faster for you. In each of the conversion<BR>\n" );
document.write( "factors you relate the equivalent amounts: 1 kg and 1000 gms, 1 ltr and 1000 ml, or any<BR>\n" );
document.write( "other equivalent amounts that you may need ... 1 ton and 2000 lbs, 1 gallon and 4 quarts,<BR>\n" );
document.write( "and so on. Then all you have to do is decide which part of the equivalence goes into the<BR>\n" );
document.write( "numerator of your conversion factor and which goes into the denominator of the conversion factor.  <BR>\n" );
document.write( "That decision depends on how you need to place them to cancel the units in the given<BR>\n" );
document.write( "problem. The more of these types of problems you do, the more logical the process<BR>\n" );
document.write( "will become to you. And you will become aware that you may need to have more conversion<BR>\n" );
document.write( "factors in the multiplication chain to work your way to the units you need in the solution.<BR>\n" );
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document.write( "Hope this helps you to work your way through this problem and others like them.<BR>\n" );
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document.write( "  </SPAN>\n" );
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