Witch number produces a rational number when added to 0.5

Any other rational number, since 0.5 is a rational number itself.

For example, 0+0.5=0.5=1/2 => rational.
1.125+0.5=1 1/8+1/2=1 5/8 => rational
pi+0.5=3.64159265  => irrational  (so pi cannot be added to 0.5 to give a rational number).