If `A=12.0cmpm0.1cmandB=8.5cmpm0.5cm`, find A + B.

Answer

To solve the problem of finding \( A + B \) where \( A = 12.0 \, \text{cm} \pm 0.1 \, \text{cm} \) and \( B = 8.5 \, \text{cm} \pm 0.5 \, \text{cm} \), we will follow these steps:

### Step 1: Identify the true values of A and B
The true values are given directly in the problem:
- \( A = 12.0 \, \text{cm} \)
- \( B = 8.5 \, \text{cm} \)

### Step 2: Calculate the sum of A and B
To find the sum \( A + B \):
\[ A + B = 12.0 \, \text{cm} + 8.5 \, \text{cm} = 20.5 \, \text{cm} \]

### Step 3: Identify the uncertainties (errors) in A and B
The uncertainties are also provided:
- The uncertainty in \( A \) is \( 0.1 \, \text{cm} \)
- The uncertainty in \( B \) is \( 0.5 \, \text{cm} \)

### Step 4: Calculate the total uncertainty in A + B
When adding measurements, the total uncertainty is found by adding the individual uncertainties:
\[ \text{Total uncertainty} = \text{Uncertainty in } A + \text{Uncertainty in } B = 0.1 \, \text{cm} + 0.5 \, \text{cm} = 0.6 \, \text{cm} \]

### Step 5: Write the final result
Combining the true value and the total uncertainty, we express the result as:
\[ A + B = 20.5 \, \text{cm} \pm 0.6 \, \text{cm} \]

### Final Answer
\[ A + B = 20.5 \, \text{cm} \pm 0.6 \, \text{cm} \]

---