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 Values and Errors
- The value of \( A \) is \( 12.0 \, \text{cm} \) with an error of \( \pm 0.1 \, \text{cm} \).
- The value of \( B \) is \( 8.5 \, \text{cm} \) with an error of \( \pm 0.5 \, \text{cm} \).

### Step 2: Add the Values
We first add the measured values of \( A \) and \( B \):
\[ A + B = 12.0 \, \text{cm} + 8.5 \, \text{cm} = 20.5 \, \text{cm} \]

### Step 3: Add the Errors
Next, we add the absolute errors of \( A \) and \( B \):
\[ \text{Total Error} = 0.1 \, \text{cm} + 0.5 \, \text{cm} = 0.6 \, \text{cm} \]

### Step 4: Write the Final Result
Combining the sum of the values and the total error, we express the result as:
\[ A + B = 20.5 \, \text{cm} \pm 0.6 \, \text{cm} \]

### Final Answer
Thus, the final result is:
\[ A + B = 20.5 \, \text{cm} \pm 0.6 \, \text{cm} \]

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