Irrational Number Generator

Discover the fascinating world of irrational numbers! Enter a rational number and we'll multiply it by Pi (π) to generate an irrational number.

Enter Rational Number:

Generated Irrational Number:

Calculation Process:

Visual Representation

You entered the rational number:

Multiplying it by Pi (π), which is approximately 3.14159..., results in the irrational number:

Irrational numbers cannot be expressed as a simple fraction and their decimal representation goes on forever without repeating.

What are Irrational Numbers?

Irrational numbers are real numbers that cannot be expressed as a simple fraction of two integers. In decimal form, they have non-repeating and non-terminating decimal expansions.

Key characteristics of irrational numbers:

Cannot be written as p/q, where p and q are integers and q ≠ 0.
Their decimal representation never ends and never repeats.

Examples of irrational numbers:

Pi (π): Approximately 3.14159... (ratio of a circle's circumference to its diameter).
Square root of 2 (√2): Approximately 1.41421...
Euler's number (e): Approximately 2.71828... (base of the natural logarithm).

This tool helps you generate irrational numbers by leveraging the property that the product of a non-zero rational number and an irrational number is always irrational. Since Pi (π) is irrational, multiplying it by any rational number (except zero) will result in an irrational number.