Question
Which of the following is irrational?
(a) 0.14
(b) 0.1416
(c) 0.1416
(d) 0.1014001400014..
Solution
Option (a): 0.14
✘ Rational
Terminating decimal → rational number.
Option (b): 0.1416
✘ Rational
Terminating decimal → rational number.
Option (c): 0.1416
✘ Rational
Same as above → rational number.
Option (d): 0.1014001400014..
✔ Irrational
This decimal is non-terminating and non-repeating (no fixed pattern), so it is irrational.
Final Answer
✔ Correct option: (d) 0.1014001400014..