If `x_(1)=100cmpm0.1cmandx_(2)=90.0cmpm0.1cm`, find their difference and the error in it.

Answer

To solve the problem, we need to find the difference between two measurements, \( x_1 \) and \( x_2 \), and then determine the error in that difference.

### Step-by-Step Solution:

1. **Identify the values and their uncertainties:**
- \( x_1 = 100 \, \text{cm} \pm 0.1 \, \text{cm} \)
- \( x_2 = 90.0 \, \text{cm} \pm 0.1 \, \text{cm} \)

2. **Calculate the difference:**
- The difference \( x_1 - x_2 \) is calculated as follows:
\[ x_1 - x_2 = 100 \, \text{cm} - 90.0 \, \text{cm} = 10.0 \, \text{cm} \]

3. **Determine the error in the difference:**
- When subtracting two measurements, the total error is the sum of the individual errors:
\[ \text{Error in } (x_1 - x_2) = \text{Error in } x_1 + \text{Error in } x_2 \]
- Therefore, we have:
\[ \text{Error} = 0.1 \, \text{cm} + 0.1 \, \text{cm} = 0.2 \, \text{cm} \]

4. **Combine the results:**
- The final result for the difference along with its error is:
\[ x_1 - x_2 = 10.0 \, \text{cm} \pm 0.2 \, \text{cm} \]

### Final Answer:
The difference \( x_1 - x_2 \) is \( 10.0 \, \text{cm} \pm 0.2 \, \text{cm} \).

---