Yes, you have to re-index the page again if you want to get the result as soon as possible. If you don't , it will be at the discretion of Googlebot as when to re-crawl and re-index your page. Luckily Google offers the opportunity to request indexing at any time. So, each time you change the density, or have done any other optimization on your site, just head over to GMT and fetch as Google and then request indexing. It always works for me and within hours or at most a day, the page is indexed again and the results reflect automatically. Now, Google says that it does not guarantee indexing of your page but in my experience as soon as you are not doing anything shady, they will index your page within a short period of time.
Regarding the keyword density tools, I only use the seoquake to see the number of time my keyword is repeated in the content. Different keyword density tools will give you different number depending on what they take into account. For instance, some tools will look for your keyword everywhere (content body, meta description, meta keyword, menu, sidebar and so one) while other will stick to the main content. Because of this, you cannot trust any of those tools as to the accuracy of the density that Google wants to see in order to better position you. So, I have to warn you that saying keyword density should x, y or z is a total bullshit. Every situation is different, even in the same niche, it depends on how much offpage action you have done with your keyword. Figuring out your optimal density is a trial and learning process. Most people who still even consider keyword density is of importance to seo will just plug a number into their page and if it does not work, they just ditch every and start cursing themselves. Here is my exact process of solving keyword density issue:
-Let's say that I suspect the density might be a problem for one of my page. (I will reason with the actual number of time the keywords is repeated in my content, not on the density itself)
-I figure out that the keyword is repeated 10 times in the main body of the page or article. From here, there are two hypotheses that need to be done. One is the keyword density is too high and therefore must be lowered; and the second the keyword density is low, in which case, we have to increase it.
-So we start with the first case. We lower the keyword count to let's say 8 times or whichever number you decide. We do so by replacing the keyword with its synonyms. We update the post and request indexing. Once the page is indexed we monitor the position of the keyword for at least one or two days to see if there is any SERP movement. If it improves then that's great and we can lower the keyword again to see how far we can go or we can just stay there if we are happy with the result. If the keyword position does not improve or even worsen, there is a possibility that the keyword density is too low and we need to increase it and this leads us to the second scenario.
-In this second scenario, we increase the word count of the keyword to let's 13 and do the same as in the first scenario. We should be able to make the same judgment as to the importance of keyword density to our ranking. We can always go back to original density. The key point here is to track everything so that you can easily revert back.
Notice that I am not saying to have 0.46% or 9.52 % density, I am talking about the actual number that the keyword is repeated in your content. You do not need to know the actual density. What you need is the result! If you repeat your keyword 100 times and it gives you a good result, what's the fucking problem with that? On the other hand, if you decide to follow @hacko's advice and have 0 keyword density, it is up to you to judge how Google treat you.
Now, all those density optimizations may have no effect on your site and this can happen because ranking encompasses many things, of which backlinks are central.
Most people may see this process as boring and time-consuming and want a magic formula or quick result. Unfortunately, there is little or no such things with Google. You have to experiment everything yourself. It would be nice if you can share your experience here, should decide to follow my process. I wish you the best of luck.
