What is the greatest number to round off 3000?

Assuming whole numbers:

If rounding to the nearest 10, it would be 3004

If rounding to the nearest 50, it would be 3024

As "to the nearest whatever" increases, so the greatest number also increases.

So the greatest "whatever to round to" to produce 3000 must be 3000, that is the question becomes:

What is the greatest number that rounds to 3000 to the nearest 3000?

Half of 3000 is 1500, so the greatest whole number that rounds to 3000 is 3000 + 1500 - 1 = 4499 (since 3000 + 1500 = 4500 would round up to 6000).

Any number such that 1500 ≤ number < 4500 will round to 3000 to the nearest 3000.