To solve the problem [tex]\((102,900 \div 12) + (170 \times 1.27)\)[/tex] and express the answer to the correct number of significant figures, follow these steps:
1. Start with the division:
[tex]\[
102900 \div 12 = 8575.0
\][/tex]
2. Next, perform the multiplication:
[tex]\[
170 \times 1.27 = 215.9
\][/tex]
3. Sum the results of the division and multiplication:
[tex]\[
8575.0 + 215.9 = 8790.9
\][/tex]
Now, we need to consider the correct number of significant figures. The initial numbers involved in the calculations are:
- 102,900 which has 4 significant figures.
- 12 which has 2 significant figures.
- 170 which has 3 significant figures.
- 1.27 which has 3 significant figures.
When we perform calculations, the final result should reflect the precision of the input numbers. The addition step should be rounded based on the number with the least significant figures in the intermediate results (other values are already significantly large enough not to limit our answer):
- 8575.0 from division has 5 significant digits
- 215.9 from multiplication has 4 significant digits
Since the least number of significant figures between these components is 4 (from 215.9), we round the final result to 4 significant figures:
Thus, the correctly rounded result is:
[tex]\[
8790.9 \rightarrow 8790
\][/tex]
So, the answer to the problem is:
[tex]\[
\boxed{8,790.9}
\][/tex]
Hence, the correct answer in this context would be:
B. [tex]$8,790.9$[/tex]
