Question

Error Analysis  Your friend says that the product of 2.4 times 10 Superscript 9 and 3 times 10 Superscript negative 6 is 7.2 times 10 Superscript negative 3. What is the correct​ product? What mistake did your friend likely​ make?
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Part 1
left parenthesis 2.4 times 10 Superscript 9 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 \( (2.4 \times 10^9) \times (3 \times 10^{-6}) \), we can use the properties of multiplication for numbers in scientific notation.

1. **Multiply the coefficients:**
\[
2.4 \times 3 = 7.2
\]

2. **Add the exponents of the powers of ten:**
\[
10^9 \times 10^{-6} = 10^{9 + (-6)} = 10^{3}
\]

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

Thus, the correct product is:
\[
7.2 \times 10^3
\]

### Mistake Analysis:
Your friend's mistake likely occurred in the power of ten. They computed \( 10^{9 + (-6)} \) incorrectly, resulting in \( 10^{-3} \) instead of \( 10^{3} \). Therefore, while they correctly found the coefficient \( 7.2 \), they incorrectly added the exponents.