## Irrational numbers

### Irrational numbers are real numbers that cannot be expressed as a fraction or ratio of two integers

Irrational numbers are real numbers that cannot be expressed as a fraction or ratio of two integers. These numbers are non-repeating and non-terminating decimals. In other words, their decimal representations go on forever without a pattern.

The most famous example of an irrational number is π (pi). Its decimal representation starts with 3.141592653589793238… and continues indefinitely without repeating. Another well-known irrational number is √2 (square root of 2), which cannot be expressed as a fraction and has a decimal representation that goes on forever without a pattern.

Irrational numbers are found ubiquitously in mathematics and have many applications. They help us describe various mathematical phenomena like measurements of circles, solutions to certain equations, and fractals. They are also essential in fields such as geometry, number theory, and calculus.

It’s important to note that irrational numbers cannot be expressed exactly as decimals but can be approximated to any desired accuracy using decimal representations. For practical purposes, they are often rounded to a certain number of decimal places.

##### More Answers:

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Understanding Rational Numbers | Definition, Examples, and Applications in Mathematics