Express `0.bar(17)` in the form of `(p)/(q)`.

Explanation

To express \(0.\overline{17}\) in the form of \(\frac{p}{q}\), we can follow these steps:

### Step-by-Step Solution:

1. **Let \(x\) be the repeating decimal:**
\[ x = 0.\overline{17} \]

2. **Identify the repeating part:**
The decimal \(0.\overline{17}\) means that "17" repeats indefinitely. We can write it as:
\[ x = 0.17171717\ldots \]

3. **Multiply by 100 to shift the decimal point:**
Since "17" has 2 digits, we multiply both sides of the equation by 100:
\[ 100x = 17.171717\ldots \]

4. **Set up the equations:**
Now we have two equations:
- Equation 1: \(x = 0.171717\ldots\)
- Equation 2: \(100x = 17.171717\ldots\)

5. **Subtract Equation 1 from Equation 2:**
To eliminate the repeating decimal, we subtract Equation 1 from Equation 2:
\[ 100x - x = 17.171717\ldots - 0.171717\ldots \]
This simplifies to:
\[ 99x = 17 \]

6. **Solve for \(x\):**
Now, divide both sides by 99 to solve for \(x\):
\[ x = \frac{17}{99} \]

7. **Final answer:**
Therefore, \(0.\overline{17}\) can be expressed as:
\[ 0.\overline{17} = \frac{17}{99} \]