The given problem is asking to divide two numbers expressed in scientific notation:

$\frac{3.5 \times 10^6}{7.0 \times 10^2}$

Step 1: Divide the coefficients

$\frac{3.5}{7.0} = 0.5$

Step 2: Subtract the exponents

When dividing powers of 10, subtract the exponent in the denominator from the exponent in the numerator: $10^6 \div 10^2 = 10^{6-2} = 10^4$

Step 3: Combine the result

Now, combine the coefficient and the power of 10: $0.5 \times 10^4$

Step 4: Adjust scientific notation

The coefficient in scientific notation should be between 1 and 10, so we adjust: $0.5 \times 10^4 = 5.0 \times 10^3$

Final Answer:

• The "a" part (mantissa) is: 5.0
• The "b" part (exponent) is: 3

Let me know if you'd like further details or clarifications!

Here are 5 related questions to expand on this:

1. How would you handle multiplication of two numbers in scientific notation?
2. What is the rule for adding and subtracting numbers in scientific notation?
3. How do you convert large numbers to scientific notation?
4. How would you adjust if the coefficient was negative, like $-3.5 \times 10^6$?
5. What are the real-world applications of scientific notation?

Tip: Always remember to adjust the coefficient to stay within the range [1, 10) when expressing results in proper scientific notation!