document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170704>Question 1170704</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let n! Equal n×(n-1) ×…×2×1. For example, 4! = 4×3×2×1 = 24. \r<BR>\n" );
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document.write( "A clerk performs the computation: 1% of 2% of 3% of … 100% of n and gets the number 99! \r<BR>\n" );
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document.write( "How many digits in n are zero? <BR>\n" );
document.write( "A) 98 b) 99 c) 198 d) 199 e) 200 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #795592 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3820)</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=795592\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "1% of 2% of 3% of ... 100% of n = 99!\r<BR>\n" );
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document.write( "0.01*0.02*0.03*...*0.99*1.00*n = 99!\r<BR>\n" );
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document.write( "(1/100)*(2/100)*(3/100)*...*(99/100)*(100/100)*n = 99!\r<BR>\n" );
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document.write( "(<font color=blue>1*2*3*...*99</font>*100)/(100^100)*n = <font color=blue>99!</font>\r<BR>\n" );
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document.write( "(<font color=blue>99!</font>*100)/(100^100)*n = <font color=blue>99!</font>\r<BR>\n" );
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document.write( "100/(100^100)*n = 1    ...... note the <font color=blue>99!</font> terms cancel\r<BR>\n" );
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document.write( "100*n = 1*100^100   \r<BR>\n" );
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document.write( "100*n = 100^100   \r<BR>\n" );
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document.write( "n = (100^100)/(100)   \r<BR>\n" );
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document.write( "n = (100^100)/(100^1)   \r<BR>\n" );
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document.write( "n = 100^(100-1)\r<BR>\n" );
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document.write( "n = 100^99\r<BR>\n" );
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document.write( "n = (10^2)^99\r<BR>\n" );
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document.write( "n = 10^(2*99)\r<BR>\n" );
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document.write( "n = 10^198\r<BR>\n" );
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document.write( "There are 198 zeros in the number n.<BR>\n" );
document.write( "n is equal to 1 followed by 198 zeros.\r<BR>\n" );
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document.write( "The exponent over 10 tells us how many zeros there are.\r<BR>\n" );
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document.write( "Consider a smaller example such as 10^3 = 1000 which has three zeros.<BR>\n" );
document.write( "Or consider 10^5 = 100,000 which has five zeros<BR>\n" );
document.write( "The number of zeros in 10^k is k.\r<BR>\n" );
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document.write( "Answer: <font color=red>C) 198</font><BR>\n" );
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