Question
Divide. Wrile your answer in scientific notation, \[ \begin{array}{l}\frac{6 \times 10^{-3}}{2 \times 10^{1}} \\ \times 10\end{array} \]
Ask by Colon Mccarthy. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The answer is \(3 \times 10^{-3}\).
Solution
To solve the expression:
\[
\frac{6 \times 10^{-3}}{2 \times 10^{1}} \times 10
\]
Follow these steps:
1. **Divide the coefficients:**
\[
\frac{6}{2} = 3
\]
2. **Subtract the exponents for the powers of 10:**
\[
10^{-3} \div 10^{1} = 10^{-3 - 1} = 10^{-4}
\]
3. **Multiply by 10 (which is \(10^1\)):**
\[
3 \times 10^{-4} \times 10^{1} = 3 \times 10^{-4 + 1} = 3 \times 10^{-3}
\]
**Final Answer in Scientific Notation:**
\[
3 \times 10^{-3}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To divide \( \frac{6 \times 10^{-3}}{2 \times 10^{1}} \), we first divide the coefficients: \[ \frac{6}{2} = 3 \] Next, we apply the rules of exponents for the \( 10 \) terms: \[ 10^{-3} \div 10^{1} = 10^{-3 - 1} = 10^{-4} \] So the result of the division is: \[ 3 \times 10^{-4} \] Now, we multiply this result by \( 10 \): \[ 3 \times 10^{-4} \times 10 = 3 \times 10^{-4 + 1} = 3 \times 10^{-3} \] Thus, the final answer in scientific notation is: \[ 3 \times 10^{-3} \]
