The decimal $0.18\overline{8}$ (with the 8 repeating) can be converted to a fraction as follows:

Let $x = 0.18\overline{8}$.

Step 1: Multiply by 10 to move the decimal point one place right.

$10x = 1.8\overline{8}$

Step 2: Multiply by 100 to move the decimal point two places right.

$100x = 18.8\overline{8}$

Step 3: Subtract the two equations.

Subtract $10x = 1.8\overline{8}$ from $100x = 18.8\overline{8}$: $100x - 10x = 18.8\overline{8} - 1.8\overline{8}$ $90x = 17$

Step 4: Solve for $x$.

$x = \frac{17}{90}$

So, $0.18\overline{8}$ as a fraction is $\frac{17}{90}$.

Would you like further details on this process or have any questions?

Here are 5 related questions to extend this topic:

1. How do you convert a non-repeating decimal to a fraction?
2. How do you convert other repeating decimals to fractions, like $0.2\overline{7}$?
3. What is the difference between a repeating and terminating decimal?
4. How do you simplify a fraction?
5. How do you convert a fraction back into a decimal?

Tip: When converting repeating decimals to fractions, identifying the repeating part of the decimal early helps simplify the process.