Question

which number produces an irrational number when added to 1/3

Answer 1

If an irrational number is added to 1/3 we will get an irrational number.

For example if we add 1.01001000100001----- is added to 1/3 we get

1.01001000100001...... + 0.33333....... = 1.34334333433334...........

It is non terminating and non recurring