document.write( "Question 933190: if 1/17=0.0588235294117647...., determine the 614th digit of the decimal expansion. \n" ); document.write( "

Algebra.Com's Answer #566671 by MathLover1(20850) $\"\"$ $\"About$

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if $\"1%2F17=0.0588235294117647....\"$ , determine the $\"614th\"$ digit of the decimal expansion. \r
\n" ); document.write( "\n" ); document.write( " $\"0.0588235294117647\"$ - here you got $\"16-digit-cycle\"$ , means you just add next cycle to first one like this
\n" ); document.write( " $\"0.0588235294117647+0588235294117647...\"$ and repeat until you got decimal $\"614\"$ digits to see which one is it...:-)\r
\n" ); document.write( "\n" ); document.write( "or do it this way:\r
\n" ); document.write( "\n" ); document.write( " $\"614%2F16=38+%2B6%2F16=38%28full_cycles%29%2B%283%2F8%29%28of_39th_cycle%29\"$ ..\r
\n" ); document.write( "\n" ); document.write( "since cycle has $\"16\"$ digits, $\"%283%2F8%2916=6\"$ digits; so, we add $\"058823\"$ from 39th full cycle,last one is digit we need and it is $\"3\"$ \r
\n" ); document.write( "\n" ); document.write( "so, the 614th digit of the decimal expansion $\"3\"$ \n" ); document.write( "

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