Write the answer for each expression using scientific notation with the appropriate number 
of significant figures.
 a. 23.096 x 90.300

To multiply the numbers \( 23.096 \times 90.300 \) and express the result in scientific notation with the appropriate number of significant figures:

1. **Multiplication**:  
   \[
   23.096 \times 90.300 = 2084.3688
   \]

2. **Determining Significant Figures**:  
   - The number \( 23.096 \) has 5 significant figures.
   - The number \( 90.300 \) has 5 significant figures.
   - Therefore, the result should be expressed with 5 significant figures.

3. **Expressing in Scientific Notation**:  
   \[
   2084.3688 \text{ rounded to 5 significant figures} = 2.0844 \times 10^3
   \]

So, the final answer in scientific notation with the appropriate number of significant figures is:
\[
\boxed{2.0844 \times 10^3}
\]

Would you like more details on this solution or have any questions?

Here are 5 relative questions for further exploration:
1. How do you determine the number of significant figures in a product?
2. What are the rules for rounding when dealing with significant figures?
3. How would you convert a large number like \( 5000000 \) into scientific notation with the correct significant figures?
4. Can you explain why \( 0.004560 \) has 4 significant figures?
5. What happens to the number of significant figures in division?

**Tip**: Always remember that trailing zeros after a decimal point are significant!

Learn how to multiply numbers using scientific notation and determine the appropriate number of significant figures. This problem involves multiplying 23.096 by 90.300 and expressing the result in scientific notation with 5 significant figures.

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