Question
Which of the following is a rational number?
(a) \( \pi \)
(b) \( \sqrt{5} \)
(c) 0.101001000100001 …
(d) 0.835835835 …
Solution
Option (a): \( \pi \)
✘ Irrational
\( \pi \) is non-terminating and non-repeating.
Option (b): \( \sqrt{5} \)
✘ Irrational
\( \sqrt{5} \) cannot be expressed as a fraction.
Option (c): 0.101001000100001 …
✘ Irrational
This is non-terminating and non-repeating.
Option (d): 0.835835835 …
✔ Rational
This is a repeating decimal, so it is rational.
Final Answer
✔ Correct option: (d) 0.835835835 …