Is π (pi) a rational or an irrational number?

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Detailed Solution

π (pi) is an irrational number because its decimal expansion is non-terminating and non-repeating.

A rational number can be expressed in the form p/q, where p and q are integers and q ≠ 0. Its decimal expansion is either terminating (e.g., 0.25) or non-terminating but repeating (e.g., 0.333…).

On the other hand, an irrational number cannot be written as a ratio of two integers. Its decimal expansion is non-terminating and non-repeating.

The value of π is approximately 3.141592653…, and it goes on forever without repeating any fixed pattern. Hence, it cannot be expressed as a fraction of two integers.

Therefore, π is classified as an irrational number.

Also Check: NCERT Solutions for Rational Number

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