Irrational Numbers

Every real number belongs to one of two sets: irrational or rational.

An irrational number is a real number that cannot be expressed in the form p divided by q, where p and q are integers, and q is not zero, while a rational number can be expressed as a fraction.

When expressed in decimal form, irrational numbers have decimal expansions that neither terminate nor repeat. Their digits continue infinitely. Rational numbers, on the other hand, either terminate or repeat.

One example of an irrational number is pi. Let's consider a circle. If we divide its circumference by its diameter, we get a constant value called pi. Whether the circle is as large as a Ferris wheel or as small as a coin, this ratio remains the same.

The decimal expansion of pi extends infinitely without forming a repeating pattern. Because of this, pi is an irrational number.

Since irrational numbers have non-terminating, non-repeating decimal expansions, we usually use approximations, such as rounding or truncation, in calculations. For example, pi can be approximated by rounding or truncation.