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

Answer

To solve the problem of finding the difference between \( x_1 \) and \( x_2 \) along with the error in that difference, we can follow these steps:

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

### Step 2: Calculate the difference
To find the difference \( D \) between \( x_1 \) and \( x_2 \):
\[ D = x_1 - x_2 = 100 \, \text{cm} - 90.0 \, \text{cm} = 10.0 \, \text{cm} \]

### Step 3: Calculate the error in the difference
When subtracting two quantities, the errors are added. Therefore, the total error \( \Delta D \) in the difference is:
\[ \Delta D = \Delta x_1 + \Delta x_2 = 0.1 \, \text{cm} + 0.1 \, \text{cm} = 0.2 \, \text{cm} \]

### Step 4: Write the final result
Combining the difference and the error, we have:
\[ D = 10.0 \, \text{cm} \pm 0.2 \, \text{cm} \]

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

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