To solve the division of [tex]\( \frac{4,568}{1.3} \)[/tex] and report the answer to the correct number of significant figures, we need to follow these steps:
1. Perform the Division:
[tex]\[
\frac{4,568}{1.3} = 3513.846153846154
\][/tex]
2. Determine the Significant Figures:
The divisor (1.3) has 2 significant figures. The answer must be reported with the same number of significant figures (2 significant figures).
3. Round the Result to 2 Significant Figures:
- The number [tex]\( 3513.846153846154 \)[/tex] in standard form is [tex]\( 3.513846153846154 \times 10^3 \)[/tex].
- Rounding [tex]\( 3.513846153846154 \)[/tex] to 2 significant figures, we look at the first two digits: 3 and 5. The third digit (1) will determine if we round up or down.
Since the third digit (1) is less than 5, we do not round up.
- The rounded number is [tex]\( 3.5 \times 10^3 \)[/tex], which is written in exponential notation as [tex]\( 3.5e+03 \)[/tex].
Therefore, the answer, reported to the correct number of significant figures, is [tex]\( 3.5 \times 10^3 \)[/tex] or [tex]\( 3.5e+03 \)[/tex].
