So I've been playing this game for about 8 months now and I thought I knew pretty much how most things worked. Anyway, I'm in the middle of my standard gigantic abundant all type game and I suddenly realized how approval bonus tiles work. The note implies that these tiles give a 100% bonus to any approval building built on that tile.
In the case of manufacturing (or research) bonuses this means that if you put a 16 MP Industrial Sector on a 300% manufacturing bonus tile you get 64 MP's of total production. This is the 16 RP's for the IS itself plus 300% of the 16 RP IS for the bonus. If there's only a factory you'd get a total of 32 MP's (8+3*8).
However, in the case of the 100% approval bonus tile the bonus isn't 100% times the approval bonus of the building, it's the approval bonus of the building plus another 100%. So a Virtual Reality Center on a 100% approval bonus tile is 140% (40+100) and not 80% (40+1*40). If an Entertainment Network with its measly 5% bonus is built on a 100% approval the actual morale bonus is 105% *not* the 10% that I had assumed. That's a big difference.
Now don't get too excited by this because all of these morale bonuses still get multiplied by the base morale of the population (40% at 20B, 20% at 25B), but this means the 'real' approval benefit at a pop of 20B of a 5% Entertainment Network on a 100% approval tile is actually 42% (1.05*0.4) versus the 'real' approval benefit of a 40% VRC at a 20B pop which is actually 16% (0.4*0.4).
Looking at Influence bonuses it turns out they work the same way. Putting a Stock Market with its 5% influence bonus on a 100% influence bonus tile gives an actual 105% influence bonus versus the 15% of an Embassy.
Finally, although I've known this for awhile and I'm sure most people do realize this, the bonus of an Economic Capital isn't anything like the bonus of a Research Capital or Manufacturing Capital. The Research and Manufacturing Capitals multiply the output of all the research or manufacturing buildings on the planet. The Economic Capital doesn't multiply the income of a planet full of Stock Markets. It's just the same as two Stock Markets on a single tile, really no big deal.