Question
Which of the following is an irrational number?
(a) 0.13
(b) 0.1315
(c) 0.1315
(d) 0.301323100523 …
Solution
Option (a): 0.13
✘ Rational
This is a terminating decimal, so it is rational.
Option (b): 0.1315
✘ Rational
This is also a terminating decimal, hence rational.
Option (c): 0.1315
✘ Rational
Same as above, terminating decimal → rational.
Option (d): 0.301323100523 …
✔ Irrational
This decimal is non-terminating and non-repeating (no fixed pattern), so it is irrational.
Final Answer
✔ Correct option: (d) 0.301323100523 …