Let's break down the problem from the image you provided:

1. The number rounded to the nearest hundred thousand is 400,000.
2. The same number rounded to the nearest ten thousand is 350,000.

Step-by-Step Solution:

1. For rounding to 400,000 (nearest hundred thousand):

   • Numbers between 350,000 and 449,999 will round to 400,000.

2. For rounding to 350,000 (nearest ten thousand):

   • Numbers between 345,000 and 354,999 will round to 350,000.

Combining these ranges:

• The number must be between 350,000 and 354,999 (because rounding to the nearest ten thousand gives 350,000).
• The same number must also be between 350,000 and 449,999 (to round to 400,000 at the nearest hundred thousand).

Intersection of the ranges:

• The number must be between 350,000 and 354,999.

Thus, the possible number lies within this range: 350,000 ≤ number ≤ 354,999.

If you want further clarification or more details, feel free to ask!

Here are five follow-up questions:

1. What would happen if the number was slightly above 354,999?
2. How does rounding to different place values affect the result?
3. Can you think of another real-life example where rounding to different places gives different results?
4. What would the number be if it rounded to 400,000 at the nearest hundred thousand but 360,000 at the nearest ten thousand?
5. Why do we round numbers differently based on context?

Tip: When solving rounding problems, always first establish the boundaries that define where a number rounds up or down based on place value.