Express each of the following as a fractions in the form ` (x) / ( y) ` where x, y , ` in 1 and y ne 0,`
` 2.overset(-) ( 476) `

Answer

To express the repeating decimal \( 2.\overline{476} \) as a fraction in the form \( \frac{x}{y} \), where \( y \neq 0 \), we can follow these steps:

### Step-by-Step Solution:

1. **Let \( x \) be the repeating decimal**:
\[ x = 2.476476476\ldots \]

2. **Multiply \( x \) by \( 1000 \)** (since the repeating part has 3 digits):
\[ 1000x = 2476.476476476\ldots \]

3. **Set up the equations**:
- Equation 1: \( x = 2.476476476\ldots \)
- Equation 2: \( 1000x = 2476.476476476\ldots \)

4. **Subtract Equation 1 from Equation 2**:
\[ 1000x - x = 2476.476476476\ldots - 2.476476476\ldots \]
This simplifies to:
\[ 999x = 2476 - 2 \]

5. **Calculate the right side**:
\[ 999x = 2474 \]

6. **Solve for \( x \)**:
\[ x = \frac{2474}{999} \]

### Final Result:
Thus, the repeating decimal \( 2.\overline{476} \) can be expressed as the fraction:
\[ \frac{2474}{999} \]