Let's analyze the math problems in the image you provided:

Question 13

"Write the population of Florida in expanded form using exponents."

• The answer appears to be written as: $(8 \times 10^7) + (8 \times 10^6) + (8 \times 10^5) + (1 \times 10^3) + (3 \times 10^2) + (1 \times 10^1)$ This means the population is $88,831,321$. Each component represents a different place value written with exponents of 10.

Question 14

"Joseph says that in the number 9,999,999, all the digits have the same value. Is Joseph correct?"

• The student's response is "No because each 9 has a different value."
  • The explanation is correct because although all digits are "9," their values differ based on their place value. For example:
    • The first "9" represents $9 \times 10^6$ (nine million),
    • The second "9" represents $9 \times 10^5$ (nine hundred thousand),
    • And so on, with each digit's value depending on its position in the number.

Would you like further details or clarification on any part of this explanation?

Here are 5 relative questions that expand on this:

1. What does it mean to write a number in expanded form?
2. How do you convert a number from expanded form back to standard form?
3. Can you provide another example of writing a number using exponents in expanded form?
4. What is place value, and why is it important in understanding large numbers?
5. How would the expanded form of 9,999,999 look?

Tip:

When writing large numbers in expanded form, remember that each digit's value depends on both the digit and its position (place value).