Irrational Numbers

Irrational Numbers

1. Definition

   • Real number that cannot be written as a simple fraction
   • Any real number that cannot be expressed as the quotient of two integers

2. Properties

   • Each irrational number can be expressed an infinite decimal expansion with no regularly repeating digit or group of digits
   • The decimal expansion of an irrational number is neither terminating nor recurring
   • Irrational numbers + Rational numbers = Rational numbers
   • Rational numbers x Irrational numbers = Irrational numbers
   • LCM, two Irrational numbers may or may not exists
   • Irrational numbers + Irrational numbers = may be Rational numbers / Irrational numbers
   • Irrational numbers x Irrational numbers = may be Rational numbers / Irrational numbers

3. Example of Irrational Numbers

   • Pi = 3.14159265358979…
   • Euler's Number = 2.71828182845904…
   • Golden Ratio = 1.61803398874989….
   • Square roots ( not all roots are irrational numbers )