Number Theory

We can apply a handy trick to solve this problem. 

Let's set a variable. Let's set $x=0.29\overline{6}$

We want to put x in terms of a fraction. 

Now, for that value of x, we have $10 x = 2.96\overline{6}$

This is important, as now we subtract x from 10x. We get

$10x-x = 2.96\overline{6}-0.29\overline{6}$

Since the repeating decimal cancels out, we have

$9 x = 2.67$. 

Now, we simply solve for x. We have

$x = \frac{2.67}{9}$

$x=\frac{2.67}{9}\times \frac{100}{100}= \frac{267}{900}$

$x = \frac{89}{300}$

Thus, our final answer is 89/300. 

Thanks! :)