Question

find the absolute error in r=(420+/-5)+(100+/-3)

Answer 1

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 \( 8 \).