To solve this problem, we need to determine the possible values for the missing digit in the number 2_00, such that when this number is rounded to the nearest thousand, it results in 2,000.
### Step-by-Step Solution:
1. Understanding Rounding to the Nearest Thousand:
- When rounding a number to the nearest thousand, if the digit in the hundreds place is between 0 and 4, the number rounds down to the lower thousand.
- If the digit in the hundreds place is between 5 and 9, the number rounds up to the higher thousand.
2. Analyzing the Given Number 2_00:
- The number can be represented as 2X00, where X is the missing digit.
- We need to determine the range of values for the digit X such that rounding results in 2,000.
3. Rounding Condition:
- Since the rounded number must be 2,000 (which means it rounds down to 2,000), the digit in the hundreds place must be between 0 and 4.
4. Identifying the Missing Digit:
- Let's list the possible values for the digit X such that the number remains within the range to round down to 2,000:
- If X = 0, the number is 2000.
- If X = 1, the number is 2100.
- If X = 2, the number is 2200.
- If X = 3, the number is 2300.
- If X = 4, the number is 2400.
- In all these cases, the number rounds to 2,000, staying within the range where it remains down-rounded, satisfying the condition for 2,000.
### Conclusion:
The possible values for the missing digit that make the number 2_00 round to 2,000 are:
[tex]\[0, 1, 2, 3, 4\][/tex]
Therefore, the possibilities for the missing digit are 0, 1, 2, 3, and 4.
