document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=980298>Question 980298</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the number of digits of expression in 6^3×4^11×5^5. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601480 by </B><A HREF=/tutors/aboutme.mpl?userid=onlinepsa><B>onlinepsa(22)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=onlinepsa><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=onlinepsa><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=601480\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the number of digits of expression in 6^3×4^11×5^5.\r<BR>\n" );
document.write( "\n" );
document.write( "6^3 × 4^11 × 5^5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "=2^3 x 3^3 × 2^22 ×5^5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "= 2^25 x 3^3 x 5^5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "= 2^20 x 3^3 x (5^5 x 2^25)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "= 2^20 x 3^3 x  [100,000]\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "= 2^20 x 27 x  [100,000]\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "= (2^10)^2 x 27 x  [100,000]\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "= (1024)^2 x 27 x  [100,000]\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To find the number of digits of 1024^2, we can take a lower value below 1024 and a higher one to see what the behaviour is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(1000)^2 = 1000*1000 = 1,000,000 [7 digits]\r<BR>\n" );
document.write( "\n" );
document.write( "(2000)^2 = 2000*2000 = 4,000,000 [7 digits]\r<BR>\n" );
document.write( "\n" );
document.write( "In any case the number of digits remain same.\r<BR>\n" );
document.write( "\n" );
document.write( "To, find the number of digits we can take 1000 in place of 1024;\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(1024)^2 x 27 x  [100,000]\r<BR>\n" );
document.write( "\n" );
document.write( "= (1000)^2 x 27 x  [100,000]\r<BR>\n" );
document.write( "\n" );
document.write( "=2,700,000,000,000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Number of digits = 13.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Thanks,<BR>\n" );
document.write( "PRD<BR>\n" );
document.write( "https://onlinepsa.wordpress.com </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );