**Convert a Repeating Decimal to a Fraction**Objective: Convert the repeating decimal \(0.\overline{83}\) to a fraction.To solve this, follow these steps:1. **Identify the repeating part**: The digits \(83\) repeat indefinitely.2. **Set up an equation**: Let \(x = 0.\overline{83}\).3. **Multiply to remove the repeat**: Multiply by 100 (since there are two repeating digits) to get: \[ 100x = 83.838383\ldots \]4. **Subtract to solve for \(x\)**: Subtract the original \(x = 0.\overline{83}\): \[ 100x - x = 83.838383\ldots - 0.838383\ldots \] This simplifies to: \[ 99x = 83 \]5. **Solve for \(x\)**: \[ x = \frac{83}{99} \]Thus, the fraction form of \(0.\overline{83}\) is \(\frac{83}{99}\).**Visual Representation:**- The fraction is represented with two placeholders: [ ? ] over [ ]. The solution filled in would be: \[ \frac{83}{99} \]

Name: **Convert a Repeating Decimal to a Fraction**Objective: Convert the r
Uploaded: 2024-03-20T06:46:03.000Z
Channel: Bartleby
Description: **Convert a Repeating Decimal to a Fraction**Objective: Convert the repeating decimal \(0.\overline{83}\) to a fraction.To solve this, follow these steps:1. **Identify the repeating part**: The digits \(83\) repeat indefinitely.2. **Set up an equati