Let's tackle this question step by step.
### Part (a)
Smallest and Greatest Possible Numbers:
To determine the smallest possible number that rounds to 3000 when rounded to the nearest thousand:
- A number will round to 3000 if it is at least halfway between 2000 and 3000.
- The halfway point is 2500. Therefore, the smallest number that would round to 3000 when rounded to the nearest thousand is 2500.
For the greatest possible number that rounds to 3000 when rounded to the nearest thousand:
- A number will round to 3000 if it is less than halfway between 3000 and 4000.
- The halfway point is 3500, but to round down to 3000, the greatest number must be just below 3500, so the greatest number is 3499.
So:
- The smallest number is 2500.
- The greatest number is 3499.
### Part (b)
Three More Possible Numbers:
We need to find three examples of different whole numbers that round to 3000 when rounded to the nearest thousand. Any number within the range from 2500 to 3499 will work. Here are three possible examples within this range:
1. 2750
2. 3000
3. 3200
In conclusion:
- Smallest possible number: 2500
- Greatest possible number: 3499
- Three more possible numbers: 2750, 3000, and 3200
