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. **Multiply both sides by 100 to shift the decimal point two places to the right:**
\[ 100x = 17.\overline{17} \]

3. **Now, we have two equations:**
- Equation 1: \( x = 0.\overline{17} \)
- Equation 2: \( 100x = 17.\overline{17} \)

4. **Subtract Equation 1 from Equation 2:**
\[ 100x - x = 17.\overline{17} - 0.\overline{17} \]
This simplifies to:
\[ 99x = 17 \]

5. **Solve for \( x \):**
\[ x = \frac{17}{99} \]

6. **Thus, \( 0.\overline{17} \) can be expressed as:**
\[ \frac{p}{q} = \frac{17}{99} \]

### Final Result:
\[ 0.\overline{17} = \frac{17}{99} \]

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