The Rational Number In The Following Is:

The correct answer is B. A rational number is one that can be written as p/q with integers p and q, q not zero. Equivalently, its decimal expansion either terminates or repeats in a block. In 2.371371..., the block "371" repeats forever, so the number is rational. It equals 2 + 371/999, which you can verify directly.

• A: 1010010001... has no terminating point and no repeating block. The number of zeros between the ones keeps growing, so it is irrational.
• C: No value is given for this option, so it cannot be treated as a valid rational choice.
• D: π is irrational. Lambert proved this in 1761, and Lindemann proved in 1882 that it is transcendental.

The core concept here is the decimal test for rationality, which is the basis for classifying real numbers. It ties into the Number System topics in Quantitative Aptitude and Mathematics in Prelims, and into the idea of incommensurable quantities in the history of mathematics.

Trap: Aspirants see a long, non-ending decimal and assume it is irrational. Always check whether a block repeats. Pattern-looking sequences like A can look orderly yet still be irrational.