document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=501623>Question 501623</A>: <I><SPAN STYLE=\"word-break: break-all;\"> my question is ...<BR>\n" );
document.write( "Which of the following is equal to 3.4 times 10 to the negative 4th power?\r<BR>\n" );
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document.write( "1. 0.34<BR>\n" );
document.write( "2. 0.034<BR>\n" );
document.write( "3. 0.0034<BR>\n" );
document.write( "4. 0.00034<BR>\n" );
document.write( "5. 3.4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #338602 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=338602\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the rules are:\r<BR>\n" );
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document.write( "each time you shift the decimal point one position to the right, you need to subtract 1 from the exponent of 10.<BR>\n" );
document.write( "conversely, each time you subtract 1 from the exponent of 10, you need to shift the decimal point one position to the right.\r<BR>\n" );
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document.write( "each time you shift the decimal point one position to the left, you need to add 1 to the exponent of 10.<BR>\n" );
document.write( "conversely, each time you add 1 to the exponent of 10, you need to shift the decimal point one position to the left.\r<BR>\n" );
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document.write( "10^0 = 1\r<BR>\n" );
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document.write( "100.0 is equivalent to 100.0 * 10^0<BR>\n" );
document.write( "shift the decimal point to the right one place and you have to subtract 1 from the exponent of 10.  the number becomes 1000.0 * 10^-1<BR>\n" );
document.write( "add 1 to the exponent of 10 and the decimal point has to be shifted to the left one time.  the number becomes 100 * 10^0.\r<BR>\n" );
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document.write( "decimal notation of a number would be:<BR>\n" );
document.write( "537.66329<BR>\n" );
document.write( "non-standard scientific notation of that same number without shifting any decimal points would be:<BR>\n" );
document.write( "537.66329 * 10^0\r<BR>\n" );
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document.write( "any number in decimal notation format will be equivalent to that number * 10^0 in non-standard scientific notation format.\r<BR>\n" );
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document.write( "the standard format of the scientific notation of any number is always 1 digit to the left of the decimal point and the rest of the digits to the right of the decimal point.<BR>\n" );
document.write( "the number 357.66329 in decimal notation format needs to be converted to the standard scientific notation format by following the rules for shifting decimal places.\r<BR>\n" );
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document.write( "we start with 537.66329 in decimal notation format.<BR>\n" );
document.write( "we multiply it by 10^0 to get it into non-standard scientific notation format.<BR>\n" );
document.write( "the number becomes:<BR>\n" );
document.write( "537.66329 * 10^0<BR>\n" );
document.write( "we need to move the decimal 2 places to the left.<BR>\n" );
document.write( "this means we also have to add 2 to the exponent of the 10.<BR>\n" );
document.write( "the standard scientific notation format of the number becomes:<BR>\n" );
document.write( "5.3766329 * 10^2\r<BR>\n" );
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document.write( "537.66329 in decimal notation format = 5.3766329 * 10^2 in standard scientific notation format.<BR>\n" );
document.write( "use your calculator to confirm that these 2 number are equivalent.<BR>\n" );
document.write( "you don't really need a calculator.<BR>\n" );
document.write( "10^2 is equal to 100.<BR>\n" );
document.write( "5.3766329 * 100 is equal to 537.66329\r<BR>\n" );
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document.write( "your problem starts out as:<BR>\n" );
document.write( "3.4 * 10^-4<BR>\n" );
document.write( "the number is in scientific notation format.<BR>\n" );
document.write( "you want to convert the number to decimal notation format.<BR>\n" );
document.write( "you need to get the 10^-4 to become 10^0 by adding 4 to the exponent.<BR>\n" );
document.write( "if you add 4 to the exponent of 10, you have to shift the decimal point 4 places to the left.<BR>\n" );
document.write( "you will wind up with .00034 * 10^0 which will become:<BR>\n" );
document.write( ".00034<BR>\n" );
document.write( "you may use your calculator to confirm that .00034 is equal to 3.4 * 10^-4.\r<BR>\n" );
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document.write( "a good reference to help you understand this better can be found here:<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.purplemath.com/modules/exponent3.htm\" target = \"_blank\">http://www.purplemath.com/modules/exponent3.htm</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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