Question

Error Analysis  Your friend says that the product of 2.3 times 10 Superscript 8 and 3 times 10 Superscript negative 6 is 6.9 times 10 Superscript negative 2. What is the correct​ product? What mistake did your friend likely​ make?
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Part 1
left parenthesis 2.3 times 10 Superscript 8 right parenthesis left parenthesis 3 times 10 Superscript negative 6 right parenthesisequals
  
enter your response here
​(Use scientific notation. Use the multiplication symbol in the math palette as​ needed.)

Answer 1

To find the correct product of \( (2.3 \times 10^8) \) and \( (3 \times 10^{-6}) \), we can use the rules of multiplying numbers in scientific notation.

1. **Multiply the coefficients**:
\[
2.3 \times 3 = 6.9
\]

2. **Add the exponents**:
\[
8 + (-6) = 2
\]

3. **Combine the results**:
\[
6.9 \times 10^2
\]

Therefore, the correct product is:
\[
6.9 \times 10^{2}
\]

**Your friend's calculation**
Your friend arrived at \( 6.9 \times 10^{-2} \). The mistake they likely made was incorrect addition of the exponents. They may have added \( 8 \) and \( -6 \) incorrectly, resulting in \( -2 \) instead of the correct \( 2 \).

So the final answer is:
\[
6.9 \times 10^2
\]