What is the greatest number that rounds to 500 when rounded to the nearest ten?

504.999 ...

Step-by-step explanation:

505 rounds to 510, but a number that is infinitessimally smaller rounds to 500.

Unfortunately, for any number you can write that rounds to 500, there are an infinite number of numbers that are greater and still less than 505.

In short, there is no "greatest number" that is less than 505-unless you put additional restrictions on it, like the number of digits that can be used to express it, for example.

I believe the answer is 549.