What does it mean when "calculating a percent of precision can be found from the ratio of your mass sensitivity to the equilibrant mass for each case."
My ratio of sensitivity is .010 kg. My equilibrant mass is .290 kg
$${.290 kg + .010 kg}$$
Would I just add them like what is shown in the equation? I didn't understand what it was stating clearly.
I think you are parsing that sentence incorrectly. You're not being asked to compare or combine two things, "the ratio of your mass sensitivity" and "the equilibrant mass"; instead you're being asked to find the ratio of two things, one of which is "your mass sensitivity" and the other is "the equilibrant mass".
Think of it like this. Suppose you find the mass of something and you find it's 100 kg. But suppose your measurement is only accurate to ±3 kg. That means you're only accurate to within $3\%$. Why $3\%$? Because $3/100 = .03 = 3\%$.