convert the recurring decimal 0.292929' as a decimal

I believe you mean as a fraction.

Multiply by 100, which yields 29.292929... .   Subtract the original decimal quantity by this number to obtain

29.  Thus:

100x=29.292929.....

      x=0.292929....

Subtract:

99x = 29

Divide both sides of equation to obtain:

x=29/99