Two rods have lengths measured as `(1.8 pm 0.2)`m and `(2.3 pm 0.1)`m. Calculate their combined length with error limits.

Explanation

To calculate the combined length of the two rods along with their error limits, we can follow these steps:

### Step 1: Identify the lengths and their uncertainties
We have two rods with the following measurements:
- Rod 1: Length \( L_1 = 1.8 \, \text{m} \) with an uncertainty of \( \pm 0.2 \, \text{m} \)
- Rod 2: Length \( L_2 = 2.3 \, \text{m} \) with an uncertainty of \( \pm 0.1 \, \text{m} \)

### Step 2: Calculate the combined length
To find the combined length \( L \) of the two rods, we simply add their lengths:
\[ L = L_1 + L_2 = 1.8 \, \text{m} + 2.3 \, \text{m} \]
Calculating this gives:
\[ L = 4.1 \, \text{m} \]

### Step 3: Calculate the combined uncertainty
When adding measurements with uncertainties, the uncertainties are also added together. Therefore, we calculate the total uncertainty \( \Delta L \) as follows:
\[ \Delta L = \Delta L_1 + \Delta L_2 = 0.2 \, \text{m} + 0.1 \, \text{m} \]
Calculating this gives:
\[ \Delta L = 0.3 \, \text{m} \]

### Step 4: Write the final result
The combined length of the two rods, including the uncertainty, can be expressed as:
\[ L = 4.1 \pm 0.3 \, \text{m} \]

### Final Answer:
The combined length of the two rods is \( 4.1 \pm 0.3 \, \text{m} \).

---