Let's solve the problem step-by-step:

The expression given is:

$\frac{3.69 \times 10^{-1}}{8.2 \times 10^{0}}$

Step 1: Divide the coefficients

The coefficients are 3.69 and 8.2, so we divide them:

$\frac{3.69}{8.2} \approx 0.45$

Step 2: Divide the powers of 10

The powers of 10 are $10^{-1}$ and $10^{0}$. When dividing powers of the same base, subtract the exponents:

$10^{-1} - 0 = 10^{-1}$

Step 3: Combine the result

Now, combine the result of the division:

$0.45 \times 10^{-1}$

Step 4: Convert to scientific notation

To express $0.45$ in proper scientific notation, we shift the decimal one place to the right, which decreases the exponent by 1:

$4.5 \times 10^{-2}$

Final Answer:

The result in scientific notation is:

$4.5 \times 10^{-2}$

Would you like any additional details or clarifications?

Here are 5 related questions to consider:

1. How do you add or subtract exponents when multiplying or dividing in scientific notation?
2. What is the difference between standard form and scientific notation?
3. How do you convert between decimal and scientific notation?
4. Can you explain why the exponent changes when you shift the decimal?
5. How does scientific notation simplify working with very large or small numbers?

Tip: When working with scientific notation, always make sure the coefficient is between 1 and 10 to maintain proper format.