Here are some examples of non-terminating irrational numbers: 1. Pi (π): 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679... 2. Euler's Number (e): 2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274... 3. Square root of 2: 1.41421356237309504880168872420969807856967187537694807317667973799... 4. Square root of 3: 1.732050807568877293527446341505872366942805253810380628055806979403776908526246868821... 5. Phi (Golden Ratio): 1.618033988749895098922425901123596169894713632835247897783185281646556486229893539681764... These numbers are irrational because they cannot be expressed as a finite decimal or fraction, and their digits never repeat in a predictable pattern.