document.write( "Question 71382: Find the Fraction form for each repeating decimal 0.010101..... \n" ); document.write( "

Algebra.Com's Answer #51054 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
let x=0.010101. Now multiply x by 100 so the decimal moves two places to the right. So 100x=1.010101, if you notice theres a similarity of .010101 between each term which can be canceled out by subtraction
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document.write( "                  100x=1.010101\r\n" );
document.write( "                   - x=0.010101      \r\n" );
document.write( "                ----------------                                           \r\n" );
document.write( "                   99x=1

\n" ); document.write( "Now just solve for x
\n" ); document.write( " $\"99x=1\"$
\n" ); document.write( " $\"x=1%2F99\"$
\n" ); document.write( "Hope that all makes sense. You can always check this by calculating 1/99 to get .010101. \n" ); document.write( "

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