So, what do you mean by "precision" is it that the voltage will not be exactly 1.16V or that the voltage will waver?

Basically both. Any change in the supply voltage will directly affect your reference voltage (attenuated by 0.232). However, most regulators are pretty stable and presumably there are no large load swings in your circuit, so for this application I guess it will do fine. You could bypass the lower resistor with a capacitor (1 - 10 uF or so) to reduce noise.

Regards,
Rob.