Certainly! Let's perform the division of [tex]\(0.97584\)[/tex] by [tex]\(5.68\)[/tex] and report the answer to the correct number of significant figures. Here's the step-by-step solution:
1. Identify the values to be divided:
- Numerator: [tex]\(0.97584\)[/tex]
- Denominator: [tex]\(5.68\)[/tex]
2. Perform the division:
[tex]\[
0.97584 \div 5.68 = 0.17180281690140847
\][/tex]
3. Determine the number of significant figures for the result:
- The numerator [tex]\(0.97584\)[/tex] has 5 significant figures.
- The denominator [tex]\(5.68\)[/tex] has 3 significant figures.
4. Since the result should be reported with the number of significant figures of the value with the least significant figures, we use 3 significant figures (from [tex]\(5.68\)[/tex]) for our result.
5. Round the result to 3 significant figures:
[tex]\[
0.17180281690140847 \approx 0.172
\][/tex]
So, the final answer is:
[tex]\[
0.97584 \div 5.68 \approx 0.172 \text{ (to 3 significant figures)}
\][/tex]
