document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170841>Question 170841</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One common use of positive and negative exponents is in writing numbers as scientific notation. for example 0.000052 can be writtrn as 5.2*10^-5. A) Use scientific notation and the law of exponents to evaluate (0.000054)(0.00000033)(0.013). Leave your answer in scientific notation. B) If a space probe travels at 12 kilometers per second for 10 years, how far will it travel? Write your answer in scientific notation. ( Assume 1 year =365)\r<BR>\n" );
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document.write( "Scientific Notation: A number is expressed in scientific notation when it is in the form a*10^n, where a is greater than or equal to 1 but less than 10 and n is an integer.\r<BR>\n" );
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document.write( "I got the first part, I think. <BR>\n" );
document.write( "5.4*10^-5<BR>\n" );
document.write( "3.3*10^-7<BR>\n" );
document.write( "1.3*10^-2=    23.17*10^-14\r<BR>\n" );
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document.write( "The second part I have no clue. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126137 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=126137\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A) \r<BR>\n" );
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document.write( "You are doing good. But to get the answer in scientific notation, the first number in front of the \"10 to the exponent\" MUST be in between 0 and 10. So the number 23.17*10^-14 must become 2.3*10^-13 since I shifted the decimal 1 spot to the left.\r<BR>\n" );
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document.write( "So the answer is 2.3*10^-13\r<BR>\n" );
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document.write( "B)\r<BR>\n" );
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document.write( "First, we need to convert 10 years into seconds (we could go the other way, but it might be confusing)\r<BR>\n" );
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document.write( "Since we're assuming that there are 365 days in a year, multiply 365 by 10 to get\r<BR>\n" );
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document.write( "365*10=3650 \r<BR>\n" );
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document.write( "So there are 3,650 days in 10 years\r<BR>\n" );
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document.write( "Now because there are 24 hours in 1 day, multiply 24 by 3,650 to get\r<BR>\n" );
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document.write( "24*3,650 = 87,600\r<BR>\n" );
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document.write( "So there are 87,600 hours in 10 years.\r<BR>\n" );
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document.write( "Since there are 60 minutes in an hour and 60 seconds in a minute, there are 60*60=3600 seconds in an hour\r<BR>\n" );
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document.write( "Now simply multiply 3,600 by 87,600 to get\r<BR>\n" );
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document.write( "3,600*87,600 = 315,360,000\r<BR>\n" );
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document.write( "So there are 315,360,000 seconds in a year\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=10 ALIGN=MIDDLE  ALT=\"t=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > years, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=315360000 ALIGN=MIDDLE  ALT=\"t=315360000\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds which in scientific notation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3.15%2A10%5E8 ALIGN=MIDDLE  ALT=\"t=3.15%2A10%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=rt ALIGN=MIDDLE  ALT=\"d=rt\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the distance rate time formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=12%283.15%2A10%5E8%29 ALIGN=MIDDLE  ALT=\"d=12%283.15%2A10%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=12 ALIGN=MIDDLE  ALT=\"r=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3.15%2A10%5E8 ALIGN=MIDDLE  ALT=\"t=3.15%2A10%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=37.8%2A10%5E8 ALIGN=MIDDLE  ALT=\"d=37.8%2A10%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=3.78%2A10%5E9 ALIGN=MIDDLE  ALT=\"d=3.78%2A10%5E9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Shift the decimal one spot to the left (this will raise the exponent by 1)\r<BR>\n" );
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document.write( "So the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=3.78%2A10%5E9 ALIGN=MIDDLE  ALT=\"d=3.78%2A10%5E9\"   DISABLED_style= \"max-width:90%; height:auto;\" > km which is 3,780,000,000 km. In words, this distance is 3 billion, 780 million kilometers. </SPAN>\n" );
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