Question

Which number produces an irrational number when added to 0.4

Answer 1

I don't think when this number is added to any other rational number would produce an irrational number

But we do know that when 0.4 is added to an irrational number it would be irrational. 
e.g; 0.4 + pi is irrational, etc, etc
So any other irrational number would make it irrational