Irrational numbers

Irrational numbers are real numbers that cannot be expressed as a simple fraction, meaning they cannot be written as a ratio of two integers. This means their decimal representations go on forever without repeating a pattern. A common example is the square root of 2, which approximately equals 1.414213..., continuing infinitely without repetition. Other examples include numbers like pi (π), which represents the ratio of a circle's circumference to its diameter. Irrational numbers fill in the gaps between rational numbers on the number line, contributing to a more complete understanding of mathematics and geometry.