Let's analyze the given scientific notation numbers to determine the correct comparisons.

a. $7.36 \times 10^{-4}$ vs. $2.01 \times 10^{-3}$

To compare, express both numbers in decimal form:

• $7.36 \times 10^{-4} = 0.000736$
• $2.01 \times 10^{-3} = 0.00201$

Since $0.000736$ is less than $0.00201$, the correct symbol is:

< (less than)

b. $3.05 \times 10^{7}$ vs. $5.033 \times 10^{6}$

Again, convert both to decimal form:

• $3.05 \times 10^{7} = 30,500,000$
• $5.033 \times 10^{6} = 5,033,000$

Since $30,500,000$ is greater than $5,033,000$, the correct symbol is:

> (greater than)

Final answers:

• a. $7.36 \times 10^{-4} < 2.01 \times 10^{-3}$
• b. $3.05 \times 10^{7} > 5.033 \times 10^{6}$

Would you like any additional explanations?

Here are 5 related questions:

1. What is scientific notation, and why is it useful?
2. How do you compare numbers in scientific notation with different exponents?
3. Can you explain how to convert numbers from scientific notation to decimal form?
4. What are the rules for multiplying numbers in scientific notation?
5. How does adding or subtracting numbers in scientific notation work?

Tip: When comparing numbers in scientific notation, always focus on the exponent first. If the exponents differ, the one with the larger exponent is greater!