Question
Multiply the following and express the result in scientific notation. \( \left.\qquad\left(8 \times 10^{3}\right)\left(9 \times 10^{9}\right)\right] \)
Ask by Bates Frazier. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The result is \( 7.2 \times 10^{13} \).
Solution
To solve the problem, multiply the coefficients and add the exponents:
1. Multiply the coefficients: 8 × 9 = 72.
2. Multiply the powers of ten: 10³ × 10⁹ = 10^(3+9) = 10¹².
So, you get:
72 × 10¹².
To express this in proper scientific notation, the coefficient must be between 1 and 10. Write 72 as 7.2 × 10¹:
72 × 10¹² = (7.2 × 10¹) × 10¹² = 7.2 × 10^(1+12) = 7.2 × 10¹³.
Therefore, the final answer in scientific notation is:
7.2 × 10¹³.
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Simplify this solution Bonus Knowledge
To multiply the numbers in scientific notation, you first multiply the coefficients (the numbers in front) and then add the exponents. So, you multiply \(8\) and \(9\) to get \(72\). Then, you add the exponents from \(10^3\) and \(10^9\): \[ 3 + 9 = 12. \] Now, we have: \[ 72 \times 10^{12}. \] However, \(72\) is not in proper scientific notation (which requires a coefficient between \(1\) and \(10\)). To convert \(72\) into scientific notation, you can write it as \(7.2 \times 10^1\). Now, combine: \[ 7.2 \times 10^1 \times 10^{12} = 7.2 \times 10^{1 + 12} = 7.2 \times 10^{13}. \] So, the final result is \(7.2 \times 10^{13}\).
