Which of the following correctly describes the nature of \(2.\overline{45}\)?

Rational number

Let \(x = 2.\overline{45}\). The repeating block has length 2, so multiply by 100: \(100x = 245.\overline{45}\). Subtracting gives \(99x = 243\), hence \(x = \frac{243}{99} = \frac{27}{11}\). This is a fraction, so the number is rational. Option B (irrational) is incorrect because irrational numbers do not have terminating or repeating decimal expansions; here the decimal repeats. Option C (non-real) is wrong because the number is real, and option D (whole number) is wrong because there is a nonzero fractional part. Exam tip: An overline means a repeating block — use multiplication by \(10^n\) (where n is block length) to convert to a fraction quickly.

This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.