Question
Which of the following is an irrational number?
(a) 3.14
(b) 3.141414 …
(c) 3.1444444…
(d) 3.14114111411114 …
Solution
Option (a): 3.14
✘ Rational
Terminating decimal → rational number.
Option (b): 3.141414 …
✘ Rational
Repeating decimal → rational number.
Option (c): 3.1444444…
✘ Rational
Non-terminating but repeating → rational number.
Option (d): 3.14114111411114 …
✔ Irrational
This decimal is non-terminating and non-repeating (no fixed pattern), so it is irrational.
Final Answer
✔ Correct option: (d) 3.14114111411114 …