If `L = 2.06 cm pm 0.02 cm,`
B=1.11 cm `pm 0.03 cm,`
then L+B equals to

Options

A. `3.17 cm pm 0.05 cm`
B. `2.06 cm pm 0.05 cm`
C. `3.17 cm pm 0.02 cm`
D. `3.17 cm pm 0.03 cm`

Explanation

To solve the problem of finding \( L + B \) along with the associated uncertainty, we can follow these steps:

### Step 1: Identify the values and uncertainties
We are given:
- \( L = 2.06 \, \text{cm} \) with an uncertainty of \( \pm 0.02 \, \text{cm} \)
- \( B = 1.11 \, \text{cm} \) with an uncertainty of \( \pm 0.03 \, \text{cm} \)

### Step 2: Calculate the sum of the lengths
To find \( L + B \):
\[ L + B = 2.06 \, \text{cm} + 1.11 \, \text{cm} \]
Calculating this gives:
\[ L + B = 3.17 \, \text{cm} \]

### Step 3: Calculate the total uncertainty
The total uncertainty when adding two measurements is the sum of their individual uncertainties:
\[ \text{Total uncertainty} = \Delta L + \Delta B \]
Where:
- \( \Delta L = 0.02 \, \text{cm} \)
- \( \Delta B = 0.03 \, \text{cm} \)

Calculating the total uncertainty:
\[ \text{Total uncertainty} = 0.02 \, \text{cm} + 0.03 \, \text{cm} = 0.05 \, \text{cm} \]

### Step 4: Write the final result
Combining the sum and the total uncertainty, we have:
\[ L + B = 3.17 \, \text{cm} \pm 0.05 \, \text{cm} \]

### Final Answer:
\[ L + B = 3.17 \, \text{cm} \pm 0.05 \, \text{cm} \]

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