Let's solve the given problems by multiplying the numbers in scientific notation.

Problem (a):

$(7.2 \times 10^8) \times (2.0 \times 10^{-3})$

1. Multiply the coefficients: $7.2 \times 2.0 = 14.4$

2. Add the exponents of 10: $8 + (-3) = 5$

So, the result is: $14.4 \times 10^5$ Now, we can adjust it to standard scientific notation by moving the decimal: $1.44 \times 10^6$

Problem (b):

$(6.0 \times 10^3) \times (3.5 \times 10^{-5})$

1. Multiply the coefficients: $6.0 \times 3.5 = 21.0$

2. Add the exponents of 10: $3 + (-5) = -2$

So, the result is: $21.0 \times 10^{-2}$ Now, adjust it to standard scientific notation: $2.1 \times 10^0$

Final Answers:

• (a): $1.44 \times 10^6$
• (b): $2.1 \times 10^0$

Would you like further details on these calculations or have any questions?

5 Related Questions:

1. How do you convert numbers to scientific notation?
2. What are the rules for multiplying numbers in scientific notation?
3. How do you add and subtract exponents when multiplying powers of 10?
4. Can you explain how to adjust the coefficient to proper scientific notation?
5. What happens when you multiply numbers with negative exponents?

Tip: Always ensure the coefficient in scientific notation is between 1 and 10 for proper formatting.