The length of a pencil is `(15.1+-0.1)` cm. A small piece of length is cut out so that the length of the remaining pencil is `(11.9+-0.2)` cm what is the length of the small piece?

Explanation

To find the length of the small piece cut from the pencil, we can follow these steps:

1. **Identify the given values**:
- The original length of the pencil (L) is \(15.1 \pm 0.1\) cm.
- The length of the remaining pencil (L1) is \(11.9 \pm 0.2\) cm.

2. **Set up the relationship**:
- The length of the small piece cut out (L2) can be found using the equation:
\[ L2 = L - L1 \]

3. **Substitute the values**:
- Substitute the values of L and L1 into the equation:
\[ L2 = (15.1 \pm 0.1) - (11.9 \pm 0.2) \]

4. **Perform the subtraction**:
- Calculate the central value:
\[ 15.1 - 11.9 = 3.2 \text{ cm} \]

5. **Calculate the uncertainty**:
- To find the total uncertainty, we add the uncertainties of L and L1:
\[ \text{Uncertainty in } L2 = 0.1 + 0.2 = 0.3 \text{ cm} \]

6. **Combine the results**:
- Thus, the length of the small piece cut out is:
\[ L2 = 3.2 \pm 0.3 \text{ cm} \]

### Final Answer:
The length of the small piece cut out is \(3.2 \pm 0.3\) cm.

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