document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208144>Question 1208144</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One light-year is defined by astronomers to be the distance that a beam of light will travel in 1 year (365 days). If the speed of light is 186,000 miles per second, how many miles are in a light-year? Express your answer in scientific notation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #846350 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=846350\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer:  <font color=red>5.87 * 10^12 miles</font><BR>\n" );
document.write( "In word form this is 5.87 trillion miles.<BR>\n" );
document.write( "This value is approximate.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Explanation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Think of \"186,000 miles per second\" as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C2%2C186000%2C%22mi%22%29%2Fmatrix%281%2C2%2C1%2C%22sec%22%29 ALIGN=MIDDLE  ALT=\"matrix%281%2C2%2C186000%2C%22mi%22%29%2Fmatrix%281%2C2%2C1%2C%22sec%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then multiply that fraction with these 4 extra conversion factors<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A%28matrix%281%2C2%2C186000%2C%22mi%22%29%2Fmatrix%281%2C2%2C1%2C%22sec%22%29%29%0D%0A%28matrix%281%2C2%2C60%2C%22sec%22%29%2Fmatrix%281%2C2%2C1%2C%22min%22%29%29%0D%0A%28matrix%281%2C2%2C60%2C%22min%22%29%2Fmatrix%281%2C2%2C1%2C%22hour%22%29%29%0D%0A%28matrix%281%2C2%2C24%2C%22hours%22%29%2Fmatrix%281%2C2%2C1%2C%22day%22%29%29%0D%0A%28matrix%281%2C2%2C365%2C%22days%22%29%2Fmatrix%281%2C2%2C1%2C%22year%22%29%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Each conversion factor is based on these facts<BR>\n" );
document.write( "60 sec = 1 min<BR>\n" );
document.write( "60 min = 1 hour<BR>\n" );
document.write( "24 hours = 1 day<BR>\n" );
document.write( "365 days = 1 year (ignoring leap years)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice very carefully how I've set up the units so that nearly everything cancels out. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A%28matrix%281%2C2%2C186000%2C%22mi%22%29%2Fmatrix%281%2C2%2C1%2Ccross%28%22sec%22%29%29%29%0D%0A%28matrix%281%2C2%2C60%2Ccross%28%22sec%22%29%29%2Fmatrix%281%2C2%2C1%2Cblue%28cross%28%22min%22%29%29%29%29%0D%0A%28matrix%281%2C2%2C60%2Cblue%28cross%28%22min%22%29%29%29%2Fmatrix%281%2C2%2C1%2Cgreen%28cross%28%22hour%22%29%29%29%29%0D%0A%28matrix%281%2C2%2C24%2Cgreen%28cross%28%22hours%22%29%29%29%2Fmatrix%281%2C2%2C1%2Cred%28cross%28%22day%22%29%29%29%29%0D%0A%28matrix%281%2C2%2C365%2Cred%28cross%28%22days%22%29%29%29%2Fmatrix%281%2C2%2C1%2C%22year%22%29%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The only thing left will be \"miles\" up top and \"years\" down below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C2%2C186000%2A60%2A60%2A24%2A365%2C%22miles%22%29%2Fmatrix%281%2C2%2C1%2A1%2A1%2A1%2C%22year%22%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C2%2C5865696000000%2C%22miles%22%29%2Fmatrix%281%2C2%2C1%2C%22year%22%29 ALIGN=MIDDLE  ALT=\"matrix%281%2C2%2C5865696000000%2C%22miles%22%29%2Fmatrix%281%2C2%2C1%2C%22year%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C4%2C5.865696%2A10%5E12%2C%22miles%22%2C%22per%22%2C%22year%22%29 ALIGN=MIDDLE  ALT=\"matrix%281%2C4%2C5.865696%2A10%5E12%2C%22miles%22%2C%22per%22%2C%22year%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C4%2C5.87%2A10%5E12%2C%22miles%22%2C%22per%22%2C%22year%22%29 ALIGN=MIDDLE  ALT=\"matrix%281%2C4%2C5.87%2A10%5E12%2C%22miles%22%2C%22per%22%2C%22year%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I'm rounding to 3 significant figures since the \"186,000\" value is also to 3 significant figures. Those zeros aren't significant.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The \"times 10^12\" portion represents \"trillion\" which means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.87%2A10%5E12 ALIGN=MIDDLE  ALT=\"5.87%2A10%5E12\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the same as saying \"5.87 trillion\".\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Light travels roughly 5.87 trillion miles in one year.<BR>\n" );
document.write( "Therefore we conclude there are roughly 5.87 trillion miles in a light-year.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "When rounding to 1 significant figure, it yields roughly 6 trillion miles in a light-year.<BR>\n" );
document.write( "Which matches with this source<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://spaceplace.nasa.gov/light-year/en/\">https://spaceplace.nasa.gov/light-year/en/</a><BR>\n" );
document.write( "Quote from the page: \"One light-year is about 6 trillion miles (9 trillion km). That is a 6 with 12 zeros behind it!\"\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Further confirmation<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.wolframalpha.com/input?i=1+lightyear+to+miles\">https://www.wolframalpha.com/input?i=1+lightyear+to+miles</a><BR>\n" );
document.write( "The result from that page is roughly 5.879 trillion miles.<BR>\n" );
document.write( "There is rounding error in our scratch work above because the \"186,000\" value is an approximation (instead the speed of light is actually closer to 186,282 miles per second; this value is also an approximation)<BR>\n" );
document.write( "Regardless of the rounding error, we get in the same ballpark at least.<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );