To solve the problem [tex]\((102,900 \div 12) + (170 \times 1.27)\)[/tex] with the correct number of significant figures, we can follow a step-by-step approach:
### Step 1: Division
First, we need to perform the division [tex]\(102,900 \div 12\)[/tex].
[tex]\[ \frac{102,900}{12} = 8575.0 \][/tex]
The result of the division is [tex]\(8575.0\)[/tex].
### Step 2: Multiplication
Next, we need to perform the multiplication [tex]\(170 \times 1.27\)[/tex].
[tex]\[ 170 \times 1.27 = 215.9 \][/tex]
The result of the multiplication is [tex]\(215.9\)[/tex].
### Step 3: Sum the Results
Now, we add the results from the division and the multiplication.
[tex]\[ 8575.0 + 215.9 = 8790.9 \][/tex]
The sum of the two results is [tex]\(8790.9\)[/tex].
### Step 4: Determine the Correct Number of Significant Figures
Next, we need to express the final result with the correct number of significant figures. In this case, we must consider the significant figures in the original numbers used in the operations. The number with the least number of significant figures will dictate the significant figures in our final result.
- [tex]\(102,900\)[/tex] has 6 significant figures (it depends on whether the trailing zeros are significant or not).
- [tex]\(12\)[/tex] has 2 significant figures.
- [tex]\(170\)[/tex] has 3 significant figures.
- [tex]\(1.27\)[/tex] has 3 significant figures.
Among these, the least number of significant figures (2) is from [tex]\(12\)[/tex].
### Step 5: Round the Result
We need to round our sum, [tex]\(8790.9\)[/tex], to the appropriate number of significant figures. Since we need to round to 2 significant figures, we round [tex]\(8790.9\)[/tex] to [tex]\(8800\)[/tex].
### Final Answer
Thus, the correct answer is:
D. 8800
