In my understanding - Google is a machine that wants us to think that it is acting as a human being 
In general - there is some human influence on their 'algos' but it's important to understand - it is still a machine! And most important is to clearly lied down - it is machine that constantly keeps upgraded and tweaked by humans.
I see where and why Joseph coming from and I see why he still is not satisfied with the answer. You know why? Because question is wrong for this community 
Everyone here wants to do good for you Joseph! And that is why you are not getting direct answer regarding correct keyword density percentage. The truth is - this number is keeping changing constantly and whatever 'density' will you apply to your article it is - DANGEROUS! There is no exact magical number but there is a safe side that works for present moment.
And to answer you directly - do not cross 1.5 - 2.0 percentage at the moment. Think about this like that - If you will apply wrong keyword density to your article you will get fired from your job.
So, how to apply correct keyword density you are asking! - you see, you asking to guarantee you something that only Google can guarantee as there is no insight - what Google will implement next and how that will affect everyone here.
One golden rule applies for this though - keep constantly updating and changing your content! As far it is the best of the best of all ranking advices what I can give you because as far as it goes now - Whenever new content is published Google clearly and immediately recognizes, responds and communicates with you via changes of you ranking positions via what!? - via keyword density,placement,decoration,website structure, credibility,visibility and all this blah,blah,blah stuff
You see - keywords are still there!
So, sorry, but there is no magical and precise pill for this! That is why question was a bit wrong.
all the best,
Jungles