Answer is -pi
Let x be this unknown number. Adding on x to pi gets us the expression x+pi
If we set x+pi equal to zero (which is a rational number) and solve for x, we get
x+pi = 0
x+pi - pi = 0 - pi
x = -pi
so adding pi to -pi will lead to 0 since
x+pi = -pi+pi = 0
