document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=97623>Question 97623</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0072509791/algebrahomeworkh>The Physical Universe</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The speed of light is 3.0 x 108 m/sec.  The Earth is 1.5 x 1011 m from the Sun.  How many seconds does it take for light to reach us from the Sun? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #71050 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=71050\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "The distance between the Earth and the Sun is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5+%2A+10%5E11 ALIGN=MIDDLE  ALT=\"1.5+%2A+10%5E11\"   DISABLED_style= \"max-width:90%; height:auto;\" > meters<BR>\n" );
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document.write( "and the speed of light is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A10%5E8 ALIGN=MIDDLE  ALT=\"3%2A10%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > meters/second.<BR>\n" );
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document.write( "To get the answer of seconds you need to have seconds in the numerator, not in the denominator<BR>\n" );
document.write( "as you were given. So since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A10%5E8 ALIGN=MIDDLE  ALT=\"3%2A10%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the number of meters light travels in 1 second,<BR>\n" );
document.write( "you put the 1 second in the numerator and the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A10%5E8 ALIGN=MIDDLE  ALT=\"3%2A10%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > meters in the denominator.<BR>\n" );
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document.write( "Therefore, you have the ratio:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281+second%29%2F%28%283%2A10%5E8%29+meters%29 ALIGN=MIDDLE  ALT=\"%281+second%29%2F%28%283%2A10%5E8%29+meters%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now to get rid of the units of meters in the denominator, you need to multiply this ratio<BR>\n" );
document.write( "by the number of meters in a numerator ... so that the units of meters in the numerator cancel <BR>\n" );
document.write( "the units of meters in the denominator of our ratio.<BR>\n" );
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document.write( "The number of units for your numerator comes from the distance between the Earth and the Sun.<BR>\n" );
document.write( "When you multiply the conversion ratio by this distance we get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281.5%2A10%5E11%29%28+meters%29+%2A+%281+second%29%29%2F%28%283%2A10%5E8%29+meters%29%29 ALIGN=MIDDLE  ALT=\"%28%281.5%2A10%5E11%29%28+meters%29+%2A+%281+second%29%29%2F%28%283%2A10%5E8%29+meters%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that the units of \"meters\" cancel:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281.5%2A10%5E11%29%2A+%28cross%28meters%29%29+%29%2A+%28%281+second%29%2F%28%283%2A10%5E8%29%2A+cross%28meters%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and you are left with the numbers in the numerator and denominator plus the units of<BR>\n" );
document.write( "second. So the problem reduces to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281.5%2A10%5E11%29%2F%283.0+%2A10%5E8%29 ALIGN=MIDDLE  ALT=\"%281.5%2A10%5E11%29%2F%283.0+%2A10%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds<BR>\n" );
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document.write( "When you divide the 1.5 by the 3.0 you get 1/2 or 0.5.  You divide the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E11 ALIGN=MIDDLE  ALT=\"10%5E11\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E8 ALIGN=MIDDLE  ALT=\"10%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > by<BR>\n" );
document.write( "simply subtracting the exponent in the term of the denominator from the exponent of the <BR>\n" );
document.write( "term in the numerator (note that they are both base 10 so you can do this) and you get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E%2811-8%29+=+10%5E3 ALIGN=MIDDLE  ALT=\"10%5E%2811-8%29+=+10%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Combining the two factors results in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5%2A10%5E3 ALIGN=MIDDLE  ALT=\"0.5%2A10%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds and multiplying the 0.5 times<BR>\n" );
document.write( "the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E3 ALIGN=MIDDLE  ALT=\"10%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to multiplying 0.5 times 1000 (or taking half of 1000). This<BR>\n" );
document.write( "results in 500 seconds as being the answer.  (Since there are 60 seconds in a minute, <BR>\n" );
document.write( "500 seconds divided by 60 is 8.3333. This means that when light leaves the Sun it takes<BR>\n" );
document.write( "8.3333 minutes to reach the Earth.)<BR>\n" );
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document.write( "So the answer to this problem is 500 seconds.  Hope this helps. Study the way in which you<BR>\n" );
document.write( "look at the units. Work backwards from the units to be in your answer. That will tell you<BR>\n" );
document.write( "what needs to be in the denominator and what needs to be in the numerator so the units cancel<BR>\n" );
document.write( "and you are left with just the units you want in your answer. Takes practice, but once<BR>\n" );
document.write( "you get it, it's very helpful in doing conversions of units.<BR>\n" );
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document.write( " </SPAN>\n" );
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