Question
Calculate. \[ \left(8 \times 10^{5}\right)\left(6 \times 10^{2}\right) \] Write your answer in scientific notation.
Ask by Daniel Ingram. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The result is \(4.8 \times 10^{8}\).
Solution
To calculate \(\left(8 \times 10^{5}\right)\left(6 \times 10^{2}\right)\) and express the result in scientific notation, follow these steps:
1. **Multiply the coefficients (the numbers before the powers of 10):**
\[
8 \times 6 = 48
\]
2. **Add the exponents of 10:**
\[
10^{5} \times 10^{2} = 10^{5+2} = 10^{7}
\]
3. **Combine the results:**
\[
48 \times 10^{7}
\]
4. **Adjust to proper scientific notation:**
Scientific notation requires the coefficient to be between 1 and 10. To adjust:
\[
48 \times 10^{7} = 4.8 \times 10^{1} \times 10^{7} = 4.8 \times 10^{8}
\]
**Final Answer:**
\[
4.8 \times 10^{8}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To calculate \( \left(8 \times 10^{5}\right)\left(6 \times 10^{2}\right) \), we can first multiply the coefficients (8 and 6) and then add the exponents of 10. 1. \( 8 \times 6 = 48 \) 2. \( 10^{5} \times 10^{2} = 10^{(5+2)} = 10^{7} \) Now combining these, we have: \[ 48 \times 10^{7} \] Next, we need to convert \( 48 \) into scientific notation, which is \( 4.8 \times 10^{1} \). Thus: \[ 48 \times 10^{7} = 4.8 \times 10^{1} \times 10^{7} = 4.8 \times 10^{(1+7)} = 4.8 \times 10^{8} \] So, the answer in scientific notation is: \[ \boxed{4.8 \times 10^{8}} \]
