Final answer:
Option D (0.555...) produces an irrational number when added to 2/5, because 2/5 is rational and 0.555... is a non-terminating, non-repeating decimal, resulting in an irrational sum.
Step-by-step explanation:
The question is asking: Which number produces an irrational number when added to 2/5? Let's evaluate each option:
- Option A (-0.4): The sum of 2/5 and -0.4 is rational because both are rational numbers.
- Option B (2/7): The sum of 2/5 and 2/7 is rational because both are rational numbers.
- Option C (5): The sum of 2/5 and 5 is rational because both are rational numbers.
- Option D (0.555...): The sum of 2/5 and 0.555... (a repeating decimal) is an irrational number because a rational number plus a non-terminating, non-repeating decimal results in an irrational number.
Therefore, option D (0.555...) is the correct answer as it produces an irrational number when added to 2/5.