To calculate the absolute error in \( r = (420 \pm 5) + (100 \pm 3) \), we first need to determine the absolute errors of the individual quantities and then combine them.
Given:
- Quantity 1: \( 420 \pm 5 \)
- Quantity 2: \( 100 \pm 3 \)
Step 1: Identify the absolute errors
- Absolute error of Quantity 1: \( \Delta A = 5 \)
- Absolute error of Quantity 2: \( \Delta B = 3 \)
Step 2: Combine the absolute errors
When adding two quantities, the absolute error of the sum is the sum of the absolute errors:
\[ \Delta r = \Delta A + \Delta B \]
\[ \Delta r = 5 + 3 = 8 \]
Step 3: Calculate the sum
Now, we can calculate the total value of \( r \):
\[ r = 420 + 100 = 520 \]
Final result
Thus, the result with its absolute error is:
\[ r = 520 \pm 8 \]
So, the absolute error in \( r \) is \( 8 \).