Question
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Divide. Write your answer in \( s \) \[ \frac{3.38 \times 10^{-22}}{6.5 \times 10^{-32}} \]

Ask by Rojas Ingram. in the United States
Mar 18,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The answer is \( 5.2 \times 10^9 \, s \).

Solution

We start with \[ \frac{3.38 \times 10^{-22}}{6.5 \times 10^{-32}}. \] **Step 1. Divide the coefficients:** \[ \frac{3.38}{6.5} = 0.52. \] **Step 2. Divide the powers of 10 (subtract the exponents):** \[ 10^{-22} \div 10^{-32} = 10^{-22 - (-32)} = 10^{10}. \] **Step 3. Combine the results:** \[ 0.52 \times 10^{10}. \] To express in standard scientific notation, we adjust so that the coefficient is between 1 and 10: \[ 0.52 \times 10^{10} = 5.2 \times 10^9. \] Thus, the answer is \[ 5.2 \times 10^9 \, s. \]

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Bonus Knowledge

To divide the numbers in scientific notation, we divide the coefficients and subtract the exponents. First, divide the coefficients: \[ \frac{3.38}{6.5} \approx 0.520 \] Next, subtract the exponents: \[ -22 - (-32) = -22 + 32 = 10 \] Now, combine the results: \[ 0.520 \times 10^{10} \] To express this in proper scientific notation, we can write: \[ 5.20 \times 10^{9} \] So, the final answer is: \[ 5.20 \times 10^{9} \, s \]

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