To solve the given problem, we need to perform a series of arithmetic operations and ensure that the final result has the correct number of significant figures.
Let's break down the problem step by step:
1. Division:
- First, we divide [tex]\( 102,900 \)[/tex] by [tex]\( 12 \)[/tex].
- This gives us:
[tex]\[
\frac{102,900}{12} = 8575.0
\][/tex]
- The division result, [tex]\( 8575.0 \)[/tex], is accurate and should be kept for later steps.
2. Multiplication:
- Next, we multiply [tex]\( 170 \)[/tex] by [tex]\( 1.27 \)[/tex].
- This gives us:
[tex]\[
170 \times 1.27 = 215.9
\][/tex]
- The multiplication result, [tex]\( 215.9 \)[/tex], is also accurate.
3. Addition:
- Now, we add the results of the division and multiplication:
[tex]\[
8575.0 + 215.9 = 8790.9
\][/tex]
4. Significant Figures:
- Since the significant figures for the division (3 significant figures from 12) and the multiplication (3 significant figures from both 170 and 1.27) both have 3 significant figures, the final answer should also be rounded to 3 significant figures.
- Therefore, we round [tex]\( 8790.9 \)[/tex] to the nearest one decimal place which gives us [tex]\( 8790.9 \)[/tex].
So, the correct answer is:
[tex]\[
\boxed{\text{\$8,790.9}}
\][/tex]
The answer that matches this result is option B.
