To determine the result of the division [tex]\(\frac{4568}{1.3}\)[/tex] and report the answer with the correct number of significant figures, we can follow these steps:
1. Understand Significant Figures:
- The significant figures in a measurement include all the digits that are known precisely, plus one last digit that is estimated.
- When performing division, the result should be reported with the same number of significant figures as the number in the division with the fewest significant figures.
2. Identify Significant Figures in the Given Numbers:
- The numerator [tex]\(4568\)[/tex] has 4 significant figures.
- The denominator [tex]\(1.3\)[/tex] has 2 significant figures.
3. Perform the Division:
- Divide the numerator by the denominator:
[tex]\[ \frac{4568}{1.3} \approx 3513.846153846154 \][/tex]
4. Round to the Correct Number of Significant Figures:
- The number with the fewest significant figures is [tex]\(1.3\)[/tex] which has 2 significant figures.
- Therefore, the result should be rounded to 2 significant figures.
- To round [tex]\(3513.846153846154\)[/tex] to 2 significant figures:
[tex]\[ \approx 3513.8 \][/tex]
So, the result of [tex]\(\frac{4568}{1.3}\)[/tex] when rounded to the correct number of significant figures is [tex]\(3513.8\)[/tex].
