#1**+1 **

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! :)

NotThatSmart Jun 18, 2024

#1**+1 **

Best Answer

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! :)

NotThatSmart Jun 18, 2024