Alright, let's tackle this problem step by step.
First, we begin with the given expression:
[tex]\[ 15.11 + (142 \times 16.5) \][/tex]
### Step 1: Multiplication
Multiply 142 by 16.5:
[tex]\[ 142 \times 16.5 = 2343.0 \][/tex]
Since multiplication should result in the same number of significant figures as the least precise number, we have 3 significant figures here. Both 142 and 16.5 have 3 significant figures. Therefore, we keep 2343.0 in its current form because it already has 4 significant figures due to the decimal point.
### Step 2: Addition
Add 15.11 to the multiplication result:
[tex]\[ 15.11 + 2343.0 = 2358.11 \][/tex]
Now, when adding numbers, the precision to consider is based on the smallest number of decimal places in the terms being added. In this case, 15.11 has two decimal places and 2343.0 has one decimal place, so our sum should have one decimal place.
However, it’s customary to round the result to the appropriate number of significant figures, especially for scientific notations:
- The result of multiplication (2343) has 4 significant figures if we consider it as 2343.0.
- In addition, the customary precision for our context implies using fewer decimal points or rounding to meaningful precision.
### Step 3: Rounding to the Nearest Appropriate Significant Figures
The final result 2358.11, considering our significant figures rules and conventions, we process rounding to significant figures after addition, possibly rounded to the nearest hundred for simplicity:
[tex]\[ 2358.11 \approx 2400 \][/tex]
### Conclusion
Given the choices and the conventions typically applied, the closest answer is:
D. 2,400
Thereby rounded to the nearest hundred.
In summary, the correct answer to the problem, when expressed to the correct number of significant figures, is indeed 2,400.
