To implement the simple approach expounded in Example 8.2.9, call the given number $M$ so that $10 M\=74.$$\stackrel{\&conjugate0;}{35}$. Then $S\=0.$$\stackrel{\&conjugate0;}{35}$ and $100 S\=35.$$\stackrel{\&conjugate0;}{35}$ and $S\=35\/99$. Hence, $10 M\=74\+35\/99$, and

 $M\=74\/10\+35\/990\=\frac{7361}{990}$ 

To obtain this same result by summing a geometric series, write the given repeating decimal as