Question

Irrational numbers can be written as
.

Answer 1

Irrational numbers can be expressed in decimal form, but they cannot be written as exact fractions (ratios of integers). In other words, an irrational number cannot be represented as \( \frac{a}{b} \) where \( a \) and \( b \) are integers and \( b \neq 0 \). Instead, irrational numbers have non-repeating, non-terminating decimal expansions.

Some common examples of irrational numbers include:

- The square root of any non-perfect square, such as \( \sqrt{2} \) or \( \sqrt{3} \).
- The mathematical constant \( \pi \) (approximately 3.14159...).
- The mathematical constant \( e \) (approximately 2.71828...).

These numbers cannot be exactly expressed as fractions, and their decimal representation continues indefinitely without repeating.