Yes, i believe that Washington D.C's petition to become the 51st state will be approved by the Congress. This is simply because Washington D.C deserves to be the 51st state. I have no problem with that since it is big and and awesome place. It should therefore be made a state on its own.
No, Washington DC's petition to become a state will not be approved because Washington DC is not a state for political reasons. The founding fathers didn't want the people who make the laws in Washington to have too much voting power. There is a good reason to keep the balance of power in the hands of many. Congress will not approve it.
The District of Columbia will never become the 51st State, at least during my lifetime. First of all, the District of Columbia is too small and not capable of being a state. Second, the process is extremely difficult and lengthy. It will never happen. Forget about it. It's a pipe dream.
The last time the U.S. added a state to the Union was in 1959. That was almost 60 years ago. I doubt we'd start splitting up our own already established states to make more. I don't even understand why anyone would want to start a petition for it in the first place.