To evaluate the expression [tex]\(\frac{-56.143}{7.16}\)[/tex] to the correct number of significant figures, we need to follow these steps:
1. Identify the significant figures in the given quantities:
- The numerator [tex]\(-56.143\)[/tex] has 5 significant figures.
- The denominator [tex]\(7.16\)[/tex] has 3 significant figures.
2. Perform the division:
- We divide [tex]\(-56.143\)[/tex] by [tex]\(7.16\)[/tex].
[tex]\[
\frac{-56.143}{7.16} \approx -7.841225352
\][/tex]
3. Determine the number of significant figures for the result:
- The result should be expressed with the same number of significant figures as the measurement with the fewest significant figures. In this case, the denominator [tex]\(7.16\)[/tex] has the fewest significant figures (3 significant figures).
4. Round the result to the correct number of significant figures:
- The initial result of [tex]\(-7.841225352\)[/tex] needs to be rounded to 3 significant figures.
[tex]\[
-7.841225352 \approx -7.84
\][/tex]
Therefore, the expression [tex]\(\frac{-56.143}{7.16}\)[/tex] evaluated to the correct number of significant figures is [tex]\(-7.84\)[/tex].
The correct answer is:
A. [tex]\(-7.84\)[/tex]
