To solve the problem [tex]\( (102,900 \div 12) + (170 \times 1.27) \)[/tex], we need to perform the following steps accurately while adhering to the rules of significant figures.
### Step-by-Step Solution:
1. Division:
Calculate [tex]\( 102,900 \div 12 \)[/tex]:
[tex]\[
\frac{102,900}{12} = 8,575.0
\][/tex]
Here, [tex]\( 102,900 \)[/tex] has 5 significant figures (for clarity: the trailing zero is significant, as it is written with five digits), and [tex]\( 12 \)[/tex] is considered to have 2 significant figures. The result should be rounded to the least number of significant figures in the inputs, which is 2. However, since we will consider significant figures later finally, let's keep the result as [tex]\( 8,575.0 \)[/tex].
2. Multiplication:
Calculate [tex]\( 170 \times 1.27 \)[/tex]:
[tex]\[
170 \times 1.27 = 215.9
\][/tex]
Here, [tex]\( 170 \)[/tex] has 2 significant figures (the trailing zero is not significant in this case), and [tex]\( 1.27 \)[/tex] has 3 significant figures. The result should be rounded to the least number of significant figures in the inputs, which is 2 as well. But for now, we keep this result as [tex]\( 215.9 \)[/tex].
3. Addition:
Add the results from the previous steps:
[tex]\[
8,575.0 + 215.9 = 8,790.9
\][/tex]
When adding or subtracting, the number of decimal places in the result should match the number of decimal places of the input with the least number of decimal places. Here, both results are considered with one decimal (though multiplying significant figures can leave it more).
### Final Adjustment for Significant Figures:
Upon combining, although the step-by-step calculations kept more figures to clearly see the impact, the significant figures rule for the final answer after both operations would be two significant figures (the least number from the operations). Thus rounding 8,790.9 to two significant figures, we get:
[tex]\[
8,800
\][/tex]
Therefore, the correct answer to the problem while considering significant figures is:
D. 8,800
