Question
14. \( \left(9.7 \times 10^{6}\right)+\left(6.7 \times 10^{5}\right) \)
Ask by Olson Ingram. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[ 1.037 \times 10^{7} \]
Solution
To add the two numbers \( \left(9.7 \times 10^{6}\right) \) and \( \left(6.7 \times 10^{5}\right) \), follow these steps:
1. **Express both numbers with the same exponent:**
\( 6.7 \times 10^{5} = 0.67 \times 10^{6} \)
2. **Add the coefficients:**
\( 9.7 \times 10^{6} + 0.67 \times 10^{6} = (9.7 + 0.67) \times 10^{6} = 10.37 \times 10^{6} \)
3. **Express the result in scientific notation:**
\( 10.37 \times 10^{6} = 1.037 \times 10^{7} \)
**Final Answer:**
\[ \left(9.7 \times 10^{6}\right) + \left(6.7 \times 10^{5}\right) = 1.037 \times 10^{7} \]
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Simplify this solution Extra Insights
To solve \( \left(9.7 \times 10^{6}\right)+\left(6.7 \times 10^{5}\right) \), we first need to express both numbers in the same power of ten. We can convert \(6.7 \times 10^{5}\) to match \(10^{6}\): \[ 6.7 \times 10^{5} = 0.67 \times 10^{6} \] Now, we can add: \[ 9.7 \times 10^{6} + 0.67 \times 10^{6} = (9.7 + 0.67) \times 10^{6} = 10.37 \times 10^{6} \] To express it in standard scientific notation, we rewrite \(10.37 \times 10^{6}\) as: \[ 1.037 \times 10^{7} \] Thus, the final answer is: \[ 1.037 \times 10^{7} \]
