I want to make the basement into a finished space with a studio apartment that will be 10' x 25'. The current cement floor slopes 6" over 25 ft, and 2" from one side to the other. The concrete is pitted in places. I have been told that if I poor concrete over this existed floor I need a minimum of 3" - which means that if I make a flat floor it will be 9" thick at one end. What can I do. Can I get away with a sloping floor?

Do you know that the apartment will be legal? Ceiling height, fire barrier ceiling, required windows, proper egress, zoning?
6" is a LOT in 25'. Pouring new concrete over old is always problematic - it doesn't adhere and then just breaks up.
You need something more expensive, a very wet pourable self-leveling compound for concrete, and you will need to add an aggregate for the depth you want. You can go from 5" to 1/4" instead of 9" to 3". 5" is the max.
You do have to smooth it out as your pour but don't have to screed it.
Put 10' of kitchen or closets at the thin end, and you don't have to go quite 25'.
Try a site like this
Self-Leveling Concrete - Duraamen | Duraamen (http://www.duraamen.com/products/self-leveling-concrete/?gclid=CNz1wr3IjbkCFcqe4AodI1EAWg)

Thanks joypulv,
Very helpful
I do think I should do something different for the first 8' where the kitchen will be and it slopes 3" out of the total 6".

The current concrete floor is eroded in some areas, down to the dirt, My partner threw some leftover concrete in one of the eroded areas, so it is no longer down to dirt. Anyway, most of the first 8' of concrete (kitchen) is good and solid, and then there are two fairly large eroded areas. If I deal separately with this, or allow some slope here - what kind of material would I use so that it will bond well and create a finished surface. - same as above?

Do we need to patch the concrete in the eroded areas?

What kind of aggregate is added - or I can find the answer at the Duraamen website?
Thanks,
Joyce

Eroded down to dirt sounds worrisome, and makes me wonder if you should jack out all the concrete, put down a much needed vapor barrier, and pour 4" of all new concrete. You could rent an electric ladder ramp for hauling concrete out of a cellar window.
That vapor barrier will be all the difference in the world between a cellar that gets damp under your kitchen and closets and one that doesn't.
You can't really patch concrete effectively for living spaces.

I understand that starting over and digging out the cement floor would be preferable - but it is beyond my budget - and I have lived in this building for 10 yrs with the current basement and there has never been a problem with dampness or moisture. Also, could there be a problem with undermining the current foundation is we were to take up the concrete up to the foundation - It has a newer foundation sistered onto the older one when they dug out the basement space to create a garage space. I would hate to create a foundation problem...

Thanks again.!

Floors don't add strength to foundation walls.

As someone who has lived in basement space, I can tell you that even what appears to be dry probably isn't when walls and fixtures and furnishings are put in. Eventually bugs by the thousands live under the bottom stud plates and along the seams where floor meets foundation. Metal rusts. Wood gets moisture and termites move in. It might take a lot longer where you are, but all ground contains moisture, and all concrete has air bubbles in it (~18%). Special paints and sealers can't fully keep back 'hydrostatic pressure' getting past them.
The industry wasn't geared for living space in basements until fairly recently, and a lot of mistakes are still being made by contractors who haven't learned.
If you won't put in a vapor barrier and maybe 3" of concrete instead of 4", pour in self leveling concrete. And maybe that vapor barrier and laminate flooring, the totally fake stuff that you can get for under a dollar a foot.
Aggregate is anything from sand to gravel, so go by whatever the product you select tells you to add - if you use self leveling concrete.
I just don't know how bad your floor is for it to adhere to.