Question
What is the quotient of \( 2.66 \times 10^{8} \) and \( 3.5 \times 10^{2} \) expressed in scientific notation? Answer Attempt 1 out of 2 Answer: \( \square \times 10 \)
Ask by Coles Murphy. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The quotient is \(7.6 \times 10^{5}\).
Solution
Calculate or simplify the expression \( \frac{2.66 \times 10^{8}}{3.5 \times 10^{2}} \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{2.66\times 10^{8}}{3.5\times 10^{2}}\)
- step1: Separate the fraction:
\(\frac{2.66}{3.5}\times \frac{10^{8}}{10^{2}}\)
- step2: Divide:
\(0.76\times \frac{10^{8}}{10^{2}}\)
- step3: Divide:
\(0.76\times 10^{8-2}\)
- step4: Evaluate:
\(0.76\times 10^{6}\)
- step5: Rewrite the number:
\(7.6\times 10^{5}\)
The quotient of \(2.66 \times 10^{8}\) and \(3.5 \times 10^{2}\) expressed in scientific notation is \(7.6 \times 10^{5}\).
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Simplify this solution Extra Insights
To find the quotient of \( 2.66 \times 10^{8} \) and \( 3.5 \times 10^{2} \), you divide the coefficients and subtract the exponents of 10. First, divide the coefficients: \[ \frac{2.66}{3.5} \approx 0.76 \] Next, subtract the exponents: \[ 10^{8 - 2} = 10^{6} \] Putting it together, you get: \[ 0.76 \times 10^{6} \] To express this in proper scientific notation, you should have a coefficient between 1 and 10. So, you convert \( 0.76 \) to \( 7.6 \) by shifting the decimal place one position to the right, meaning you decrease the exponent by 1: \[ 7.6 \times 10^{5} \] Thus, the answer is \( 7.6 \times 10^{5} \).
