To solve the division problem [tex]\(\frac{4,568}{1.3}\)[/tex] and report the answer with the correct number of significant figures, we can follow these steps:
1. Identify the significant figures in the given numbers:
- The numerator [tex]\(4,568\)[/tex] has 4 significant figures.
- The denominator [tex]\(1.3\)[/tex] has 2 significant figures.
2. Perform the division:
[tex]\[
\frac{4,568}{1.3} \approx 3513.8461
\][/tex]
3. Determine the correct number of significant figures for the result:
- In multiplication and division, the result should be reported with the same number of significant figures as the number in the calculation with the fewest significant figures.
- Here, the number with the fewest significant figures is [tex]\(1.3\)[/tex] (2 significant figures).
4. Round the result to 2 significant figures:
- The number [tex]\(3513.8461\)[/tex] rounded to 2 significant figures is [tex]\(3500\)[/tex].
Therefore, the result of [tex]\(\frac{4,568}{1.3}\)[/tex], reported to the correct number of significant figures, is [tex]\(3500\)[/tex].
