document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=992047>Question 992047</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which pair of numbers is closer together? 10^10 and 10^50 , or the pair 10^100 and 10^101?\r<BR>\n" );
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document.write( "I know 10^100 and 10^101 are much much further apart due to the exponent operating on a much larger scale, but I don't know how to prove this is mathematical notation. My calculator gives maths error for 10^101-10^100, so ideally I would like some algebraic way of proving the solution that doesn't simply rely on typing the numbers in.\r<BR>\n" );
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document.write( "Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #611687 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=611687\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Which pair of numbers is closer together? 10^10 and 10^50 , or the pair 10^100 and 10^101? <BR>\n" );
document.write( "I know 10^100 and 10^101 are much much further apart due to the exponent operating on a much larger scale, but I don't know how to prove this is mathematical notation. My calculator gives maths error for 10^101-10^100, so ideally I would like some algebraic way of proving the solution that doesn't simply rely on typing the numbers in. <BR>\n" );
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document.write( "10^50-10^10 = 10^10[10^40-1]<BR>\n" );
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document.write( "10^101-10^100 = 10^100[10-1] = 10^10[10^90]*9<BR>\n" );
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document.write( "Since 10^90*9 > 10^40-1, 10^101-10^100 is a greater difference.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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