How important is lathe chuck run out?

Hi Guys,

There are a few three, four and six jaw scroll chucks available in a range of sizes.
A friend of mine has a six inch six jaw scroll chuck, he says is great for thin stuff. He also has a set of soft jaws for it, for when he needs high second op accuracy.

I also use soft jaws on my three jaws scroll chuck when I need to, such as boring out a gear.
 
I've wanted to get 4 jaw self centering chuck anyway. This is my lathe:

http://www.grizzly.com/products/Grizzly-7-x-12-Mini-Metal-Lathe/G8688

It comes with a 3" chuck with 3 jaws.

Can I upgrade my lathe to use a 4" or larger chuck? How do I know it'll fit my lathe? I see some chucks on Amazon, but not sure which one would fit my lathe and also which one would be an "upgrade" with less runout
Be aware that a 4 jaw self centering chuck has the same runout issues as a 3 jaw chuck. Most use a 4 jaw chuck because of the the ability to adjust each jaw independently and thus achieve zero runout.

Aside from the ability to accurately set up second operations, another use for the four jaw would be to mount previously machined parts for remachining. An example might be a shaft that needs a bearing surface remachined. It is important that the new surface be concentric with the original machining and the 4 jaw chuck permits that alignment.

A four jaw chuck still has the potential for angular runout. You can zero runout at one position on the work, usually near the chuck jaws. If there is angular runout, you will see see it at positions other than the adjustment position.

Kieth Fenner has a number of excellent YouTube videos on setting up work in a 4 jaw chuck.
 
I remember last summer or spring some guys here bought four jaw independent chuck's that could also be used like a scroll chuck.
They’re nice but expensive;a 4 jaw scroll chuck with a set-tru ability
 
Marc LeCuyer makes some great points about work holding in his 2 part video:

 
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