If `x=10.0pm0.1` and `y=10.0pm0.1`, then 2x-2y is equal to

Options

A. `(0.0pm0.1)`
B. Zero
C. `(0.0pm0.4)`
D. `(20pm0.2)`

Answer

To solve the problem where \( x = 10.0 \pm 0.1 \) and \( y = 10.0 \pm 0.1 \), and we need to find the value of \( 2x - 2y \), we will follow these steps:

### Step-by-Step Solution:

1. **Identify the values of \( x \) and \( y \)**:
- Given \( x = 10.0 \pm 0.1 \)
- Given \( y = 10.0 \pm 0.1 \)

2. **Calculate \( 2x \)**:
\[ 2x = 2 \times (10.0 \pm 0.1) = 20.0 \pm 0.2 \]
- The uncertainty in \( 2x \) is calculated as \( 2 \times 0.1 = 0.2 \).

3. **Calculate \( 2y \)**:
\[ 2y = 2 \times (10.0 \pm 0.1) = 20.0 \pm 0.2 \]
- Similarly, the uncertainty in \( 2y \) is also \( 0.2 \).

4. **Subtract \( 2y \) from \( 2x \)**:
\[ 2x - 2y = (20.0 \pm 0.2) - (20.0 \pm 0.2) \]
- When performing the subtraction, the absolute values are subtracted, but the uncertainties are added:
\[ 2x - 2y = 20.0 - 20.0 \pm (0.2 + 0.2) = 0.0 \pm 0.4 \]

5. **Final Result**:
\[ 2x - 2y = 0.0 \pm 0.4 \]

### Conclusion:
The final result is \( 2x - 2y = 0.0 \pm 0.4 \).