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On the other hand, irrational numbers cannot be expressed as fractions. Their decimal expansion is non-terminating and non-repeating, making them distinct and fascinating. A renowned example of an irrational number is Pi (π), which is approximately 3.14159 and continues infinitely with no repeating patterns. Another interesting approximation of Pi is ( \frac{22}{7} ), which gives a repeated decimal but is a rational number and therefore not a true representation of Pi.
Irrational numbers are characterized by their inability to be expressed in fraction form, and they often appear in mathematical calculations involving geometry and calculus.