Question
The decimal expansion that a rational number cannot have is:
(a) 0.25
(b) \(0.25\overline{28}\)
(c) \(0.\overline{2528}\)
(d) 0.5030030003…
Solution
A rational number has decimal expansion that is either:
- Terminating
- Non-terminating but repeating
Option (a): 0.25
✔ Possible
Terminating decimal → Rational
Option (b): \(0.25\overline{28}\)
✔ Possible
Repeating decimal → Rational
Option (c): \(0.\overline{2528}\)
✔ Possible
Repeating block → Rational
Option (d): 0.5030030003…
✘ Not Possible
This decimal is non-terminating and non-repeating (no fixed repeating pattern), so it is irrational.
Final Answer
✔ Correct option: (d) 0.5030030003…