Let's solve the given problem step-by-step to find the correct answer expressed to the right number of significant figures.
The problem is: [tex]\((102,900 \div 12) + (170 \times 1.27)\)[/tex]
1. Perform the division [tex]\(102,900 \div 12\)[/tex]:
[tex]\[
102,900 \div 12 = 8575
\][/tex]
This result has 4 significant figures (8575).
2. Perform the multiplication [tex]\(170 \times 1.27\)[/tex]:
[tex]\[
170 \times 1.27 = 215.9
\][/tex]
This result has 3 significant figures because it depends on the number with the fewest significant figures (170).
3. Add the two results together:
[tex]\[
8575 + 215.9 = 8790.9
\][/tex]
4. Round the result to the correct number of significant figures:
In this addition, the result should be rounded to the fewest number of significant figures used in components. Since [tex]\(170 \times 1.27\)[/tex] has 3 significant figures, the final result should also be expressed to 3 significant figures.
[tex]\[
8790.9 \approx 8800
\][/tex]
5. Select the correct answer:
Among the options provided:
- A. 8,790 (Incorrect)
- B. 8,790.9 (Incorrect)
- C. 8,791 (Incorrect)
- D. 8,800 (Correct)
Thus, the correct answer to the problem expressed to the correct number of significant figures is:
[tex]\[
\boxed{8800}
\][/tex]
