Question
Divide the following numbers in scientific notation and express the result in scientific notation to one decimal place, if necessary. \[ \frac{4 \times 10^{7}}{5 \times 10^{4}} \]
Ask by Chadwick Campbell. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The result is \( 8.0 \times 10^{2} \).
Solution
To divide the numbers, start by dividing the coefficients and subtracting the exponents:
1. Divide the coefficients: 4 ÷ 5 = 0.8
2. Subtract the exponents: 7 - 4 = 3
Thus, you get 0.8 × 10^3. However, for proper scientific notation the coefficient should be between 1 and 10. Convert 0.8 × 10^3 to proper scientific notation by moving the decimal point:
0.8 × 10^3 = 8.0 × 10^2
So, the final answer is 8.0 × 10^2.
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Simplify this solution The Deep Dive
To divide two numbers in scientific notation, you divide the coefficients and subtract the exponents. So, for \(\frac{4 \times 10^{7}}{5 \times 10^{4}}\): 1. Divide the coefficients: \(\frac{4}{5} = 0.8\) 2. Subtract the exponents: \(7 - 4 = 3\) Putting it all together: \[ \frac{4 \times 10^{7}}{5 \times 10^{4}} = 0.8 \times 10^{3} \] To express this in proper scientific notation, you need the coefficient to be between 1 and 10. Therefore, you can adjust it: \[ 0.8 \times 10^{3} = 8.0 \times 10^{2} \] The final answer is: \[ 8.0 \times 10^{2} \]
