Puzzle #217: Bleach

I encountered this problem at work recently.

You have some bleach which is 4.1% sodium hypochlorite (and thus 95.9% water). You need to dilute the bleach so it is 3% sodium hypochlorite.

If you start with 100 parts bleach, how many parts water (to the nearest integer) are needed to dilute to 3%? There is a simpler form that is close to 100:x; what is that?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, August 2, 2017 at noon Pacific Time. I will post the answer shortly after.