`1.2 + 3.45 + 6.789 = 11.439 ~~ 11.4`
Here, the least number of significant digits after the decimal is one. Hence, the result will be 11.4.(when rounded off to smallest number of decimal places).

Answer

To solve the problem of adding the numbers 1.2, 3.45, and 6.789 and determining the correct number of significant figures in the result, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Numbers:**
We have three numbers to add:
- \( a = 1.2 \)
- \( b = 3.45 \)
- \( c = 6.789 \)

2. **Perform the Addition:**
We add the three numbers together:
\[ a + b + c = 1.2 + 3.45 + 6.789 \]
Calculating this gives:
\[ 1.2 + 3.45 = 4.65 \]
Then adding \( 6.789 \):
\[ 4.65 + 6.789 = 11.439 \]

3. **Determine the Number of Decimal Places:**
Next, we need to determine the least number of decimal places in the original numbers:
- \( 1.2 \) has **1 decimal place**
- \( 3.45 \) has **2 decimal places**
- \( 6.789 \) has **3 decimal places**

The least number of decimal places among these is **1** (from \( 1.2 \)).

4. **Round the Result:**
Since the result \( 11.439 \) must be rounded to the least number of decimal places (which is 1), we round \( 11.439 \):
- The first decimal place is \( 4 \) (from \( 11.4 \)), and since the next digit (3) is less than 5, we do not round up.

Therefore, the rounded result is:
\[ 11.439 \approx 11.4 \]

5. **Final Result:**
The final answer, with the correct significant figures, is:
\[ 11.4 \]