document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=70909>Question 70909</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/013052316X/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Light travels through space at a constant speed of about 3*10^5 km/s. Sunlight reflecting from the moon takes about 1.28*10^0s to reach Earth. Find the distance from the moon to the Earth. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #50659 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=50659\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An equation used very often in physics is that Distance = Rate * Time<BR>\n" );
document.write( ".<BR>\n" );
document.write( "For this problem we are given that the rate or speed of light is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A10%5E5 ALIGN=MIDDLE  ALT=\"3%2A10%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" > km/s. <BR>\n" );
document.write( "We are also told that light coming to the Earth from the moon takes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.28%2A+10%5E0 ALIGN=MIDDLE  ALT=\"1.28%2A+10%5E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "seconds to make the trip.<BR>\n" );
document.write( ". <BR>\n" );
document.write( "We can substitute these two values into the distance equation and use a units check to<BR>\n" );
document.write( "make sure the units check out.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We write the equation as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+%283%2A10%5E5%29%2A%281.28%2A10%5E0%29%28km%2Fs%29%2A%28s%2F1%29 ALIGN=MIDDLE  ALT=\"D+=+%283%2A10%5E5%29%2A%281.28%2A10%5E0%29%28km%2Fs%29%2A%28s%2F1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let's clear the units first. Note that the s in the numerator (over 1) cancels with the<BR>\n" );
document.write( "s in the denominator of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=km%2Fs ALIGN=MIDDLE  ALT=\"km%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > and we are left with km as the units of the answer.<BR>\n" );
document.write( "We hold in mind that the units of the answer will be km and now drop the units from<BR>\n" );
document.write( "the equation.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Next we group the numerical multiplications together into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A1.28 ALIGN=MIDDLE  ALT=\"3%2A1.28\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The result of that<BR>\n" );
document.write( "multiplication is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.84 ALIGN=MIDDLE  ALT=\"3.84\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We in turn multiply that by the product of the exponential<BR>\n" );
document.write( "tens terms ... that product being <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E5%2A10%5E0 ALIGN=MIDDLE  ALT=\"10%5E5%2A10%5E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. When we multiply common base terms that<BR>\n" );
document.write( "have exponents, we do so by just adding the exponents.  So the multiplication becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E5%2A10%5E0=10%5E%285%2B0%29+=+10%5E5 ALIGN=MIDDLE  ALT=\"10%5E5%2A10%5E0=10%5E%285%2B0%29+=+10%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Putting everything together we get an answer of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.84%2A10%5E5 ALIGN=MIDDLE  ALT=\"3.84%2A10%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" > km<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand how to handle numbers that are associated with powers<BR>\n" );
document.write( "of 10 and also how to use units to see if the dimensions check out OK. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );