Sure, let's break down the multiplication step-by-step.
1. Identify the given values:
- We have [tex]\(3.4 \times 10^{-5}\)[/tex]
- We also have [tex]\(7.1 \times 10^8\)[/tex]
2. Multiply the significant figures:
- First, calculate the product of the decimal numbers [tex]\(3.4\)[/tex] and [tex]\(7.1\)[/tex]:
[tex]\[
3.4 \times 7.1 = 24.14
\][/tex]
3. Add the exponents:
- Next, combine the exponents of 10:
[tex]\[
10^{-5} \times 10^8 = 10^{-5+8} = 10^3
\][/tex]
4. Combine the results:
- Now, we multiply the result from the significant figures by the result of the exponents:
[tex]\[
24.14 \times 10^3
\][/tex]
5. Express the final product:
- Finally, simplify the expression:
[tex]\[
24.14 \times 10^3 = 24140
\][/tex]
Therefore, the product of [tex]\(3.4 \times 10^{-5}\)[/tex] and [tex]\(7.1 \times 10^8\)[/tex] is [tex]\(24,140\)[/tex].
