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 least possible number it could be?

Let's analyze the problem step by step:

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 the number was rounded to the nearest thousand, it was rounded to the nearest hundred. 
   - To make sure the number rounds to 7000 when rounded to the nearest thousand, the number after rounding to the nearest hundred must be between 6500 and 7499 as well.

3. **Rounding to the Nearest Ten:**
   - Before the number was rounded to the nearest hundred, it was rounded to the nearest ten.
   - The number that rounds to the nearest hundred (from 6500 to 7499) should be in a specific range where it rounds correctly after each step.

To find the least possible number, we need to identify the smallest number that when rounded to the nearest ten, then to the nearest hundred, and finally to the nearest thousand, will end up as 7000.

- **Start with the largest possible range before rounding:** 
  - For the final number to be 7000 when rounded to the nearest thousand, it must be in the range from 6500 to 7499.

- **Consider the smallest possible number:**
  - For the number to round to 6500 when rounded to the nearest hundred, it must be between 6450 and 6549.
  - The smallest number that rounds to 6500 when rounded to the nearest ten is 6450.

Therefore, **6450** is the least possible number that could satisfy all the conditions:

- 6450 rounds to 6450 (nearest ten).
- 6450 rounds to 6500 (nearest hundred).
- 6500 rounds to 7000 (nearest thousand).

Thus, the least possible number is **6450**.

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 largest possible number that could satisfy the same conditions?
2. How does rounding to different decimal places affect the final outcome?
3. Can you demonstrate a similar problem with different rounding criteria?
4. What would be the result if the rounding steps were reversed?
5. How would the solution change if the rounding was to the nearest 50 instead of 10?

**Tip:** When dealing with multiple rounds of rounding, always consider the effect of each rounding step on the subsequent ones.

Explore how to solve the problem of rounding a number first to the nearest ten, then to the nearest hundred, and finally to the nearest thousand resulting in 7000. Understand the step-by-step process and calculations involved. Suitable for Grades 6-8.

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