Certainly! Let's go through the multiplication of 0.0030 and 8.65 step by step, making sure to report the final answer with the correct number of significant figures.
1. Identify the number of significant figures in each factor:
- The number [tex]\(0.0030\)[/tex] has two significant figures (the leading zeros are not significant, but the trailing zero is because it follows a decimal point).
- The number [tex]\(8.65\)[/tex] has three significant figures.
2. Perform the multiplication:
[tex]\[
0.0030 \times 8.65
\][/tex]
3. Calculate the product:
[tex]\[
0.0030 \times 8.65 = 0.02595
\][/tex]
4. Determine the correct number of significant figures for the product:
- The rule for multiplication is that the result should have the same number of significant figures as the factor with the fewest significant figures.
- Here, the factor with the fewest significant figures is [tex]\(0.0030\)[/tex] with two significant figures.
5. Round the product to the correct number of significant figures:
- The product [tex]\(0.02595\)[/tex] needs to be rounded to two significant figures.
- When rounding [tex]\(0.02595\)[/tex] to two significant figures, we get [tex]\(0.026\)[/tex]. However, since the number prior to rounding up would affect the significant digits, it rounds to [tex]\(0.03\)[/tex] to maintain the two significant figures in this context.
Therefore, the result of [tex]\(0.0030 \times 8.65\)[/tex] reported to the correct number of significant figures is:
[tex]\[
0.03
\][/tex]
