To determine which options correspond to numbers that can be written as a number times $10^6$ in scientific notation:

Scientific Notation Form:

In scientific notation, a number is written as: $a \times 10^n$ where $1 \leq a < 10$ and $n$ is an integer. Numbers times $10^6$ must have $n = 6$, meaning they must fall within the range: $1,000,000 \leq \text{number} < 10,000,000$

Analysis of Each Option:

1. Option A: $1,456,718$

   • In scientific notation: $1.456718 \times 10^6$
   • $n = 6$, so this is a valid choice.

2. Option B: $987,654$

   • In scientific notation: $9.87654 \times 10^5$
   • $n = 5$, so this is not valid.

3. Option C: $34,587,195.33$

   • In scientific notation: $3.458719533 \times 10^7$
   • $n = 7$, so this is not valid.

4. Option D: $6,734,245.12$

   • In scientific notation: $6.73424512 \times 10^6$
   • $n = 6$, so this is a valid choice.

Correct Answers:

• A and D

Let me know if you need further details or have questions!

Expanding Questions:

1. What is the difference between $10^6$ and $10^7$ in scientific notation?
2. How can you quickly identify the power of 10 for a given large number?
3. Why does scientific notation require $1 \leq a < 10$?
4. How would you convert a decimal (e.g., $0.000456$) to scientific notation?
5. What are some real-world examples of when scientific notation is used?

Tip: Always check the power of 10 by counting how many places the decimal moves when converting a number to $a \times 10^n$.