- A0.101001000100001... (zeros increasing)
- B0.272727...
- C0.5
- D0.123123123...
Step-by-Step Solution
A decimal with a pattern that never settles into a fixed repeating block (here the number of zeros keeps increasing) is non-terminating non-recurring, hence irrational. The others are terminating or recurring (rational).
Answer: A) 0.101001000100001... (zeros increasing)