Continued Fraction Expansion

The process

• Separate the integer part
• Find the inverse of the remaining part. Result will be greated than 1.
• Repeat the process for the remaining part.

Finite expansion

Take for example.

As is finite, its continued fraction expansion is also finite. And it can be written as .

Infinite expansion

For irrational numbers, the expansion will be infinite.

For example :

Conintued fraction expansion of is .