Alright, let's go through the process of solving the problem step by step.
1. Identify the numbers: We need to multiply [tex]\(0.34\)[/tex] and [tex]\(0.568\)[/tex].
2. Multiply the numbers: Performing the multiplication of [tex]\(0.34\)[/tex] and [tex]\(0.568\)[/tex]:
[tex]\[
0.34 \times 0.568 = 0.19311999999999999
\][/tex]
3. Determine significant figures: We need to report our final answer to the correct number of significant figures. The number of significant figures in our result will be determined by the number with the fewest significant figures in the original problem:
- [tex]\(0.34\)[/tex] has 2 significant figures.
- [tex]\(0.568\)[/tex] has 3 significant figures.
Therefore, the result should be reported with 2 significant figures, as [tex]\(0.34\)[/tex] is the least precise with 2 significant figures.
4. Round the result: We now round [tex]\(0.19311999999999999\)[/tex] to 2 significant figures:
[tex]\[
0.19311999999999999 \approx 0.19
\][/tex]
Thus, the answer to [tex]\(0.34 \times 0.568\)[/tex], reported to the correct number of significant figures, is [tex]\(0.19\)[/tex].
