a number is rounded first to the nearest ten, then that new number is rounded to the nearest hundred, then that new number, when rounded to the nearest thousand, is 7000. what is the greatest possible number it could be?

Let's approach the problem step by step again, this time focusing on finding the greatest possible number that meets the criteria.

1. **Final Rounding to the Nearest Thousand:**
   - The number rounds to 7000 when rounded to the nearest thousand.
   - This means the original number must be between 6500 and 7499, inclusive.

2. **Rounding to the Nearest Hundred:**
   - Before being rounded to the nearest thousand, the number was rounded to the nearest hundred.
   - To ensure that the number rounds to 7000 when rounded to the nearest thousand, the number after rounding to the nearest hundred must still be between 6500 and 7499.

3. **Rounding to the Nearest Ten:**
   - The original number is first rounded to the nearest ten before it is rounded to the nearest hundred.
   - We need to find the largest possible original number that, after rounding to the nearest ten, then to the nearest hundred, and finally to the nearest thousand, rounds to 7000.

### Analyzing the Greatest Possible Number:

- **Starting with the final step:**
  - The largest number that rounds to 7000 when rounded to the nearest thousand is 7499.

- **Considering the nearest hundred rounding:**
  - To round to 7000, the number after rounding to the nearest hundred should be between 6500 and 7499.
  - The largest number that rounds to 7499 when rounded to the nearest hundred is 7499 itself, which implies it must round to 7500 when rounded to the nearest hundred.
  - To round to 7500, the number before rounding to the nearest hundred must be between 7450 and 7549.

- **Considering the nearest ten rounding:**
  - The largest number that rounds to 7490 when rounded to the nearest ten is 7494.
  - So, the original number must be between 7450 and 7494.

Therefore, **7494** is the greatest possible number that satisfies all the conditions:

- 7494 rounds to 7490 (nearest ten).
- 7490 rounds to 7500 (nearest hundred).
- 7500 rounds to 7000 (nearest thousand).

Thus, the greatest possible number is **7494**.

Would you like more details or have any questions about this solution? Here are some additional related questions you might find useful:

1. What is the least possible number that could satisfy the same conditions?
2. How do different rounding sequences affect the final outcome?
3. What happens if the number is rounded in a different order (e.g., first to the nearest hundred, then to the nearest ten)?
4. Can you demonstrate a scenario where the number rounds to 8000 instead of 7000?
5. How would the solution change if the rounding was to the nearest 5 instead of 10?

**Tip:** When determining the range of numbers that meet a series of rounding conditions, consider the cumulative effects of each rounding step.

Explore how to find the greatest possible number that rounds first to the nearest ten, then to the nearest hundred, and finally to 7000 when rounded to the nearest thousand. This problem involves sequential rounding of numbers and understanding numerical ranges. Suitable for students in Grades 4-6.

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