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Let's solve the expression:

\[
\frac{3 \times 10^5}{1 \times 10^8} \times 5
\]

### Step 1: Simplify the Fraction
The fraction can be simplified by dividing \(3 \times 10^5\) by \(1 \times 10^8\):

\[
\frac{3 \times 10^5}{1 \times 10^8} = 3 \times 10^{5 - 8} = 3 \times 10^{-3}
\]

### Step 2: Multiply by 5
Now we take the result \(3 \times 10^{-3}\) and multiply it by 5:

\[
3 \times 10^{-3} \times 5 = (3 \times 5) \times 10^{-3} = 15 \times 10^{-3}
\]

### Step 3: Express in Standard Form
To express this result in standard form:

\[
15 \times 10^{-3} = 1.5 \times 10^{-2}
\]

### Final Answer:
\[
\frac{3 \times 10^5}{1 \times 10^8} \times 5 = 1.5 \times 10^{-2}
\]

Would you like further details on any step, or have any questions?

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### Related Questions:
1. How can we simplify expressions with powers of 10?
2. What are the properties of exponents used in these calculations?
3. How can scientific notation help in calculations with very large or very small numbers?
4. Why is \(10^{-3}\) considered a small number and how does it affect multiplication?
5. What other types of problems involve multiplication and division of powers of ten?

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### Tip:
When dealing with powers of 10, remember that multiplying powers involves adding exponents, while dividing powers involves subtracting exponents. This can simplify your work significantly!

Evaluate \( \frac{3 \times 10^5}{1 \times 10^8} \times 5 \)

Learn how to evaluate the expression \( \frac{3 \times 10^5}{1 \times 10^8} \times 5 \) using scientific notation. This solution explains key concepts in exponent rules, including dividing and multiplying powers of 10. Suitable for students in Grades 9-10.

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