Calculate Infinite Continued Fractions - Definition, Formula and Example

Definition:

An irrational number can be described as an infinite continued fraction. Portrayal of an irrational number is necessary as its primary values proffer the required rational approximations to that number. The series of values never ends in the infinite continued fraction.

Formula:



Example:
Consider any fraction value for e.g. 4/5. Assume value for a0 as '0', value for a1 as '1/0.8' and value for a2 as '1/0.25'. Find the infinite continued fractions value?

Given,
Fraction value = 4/5,
a0 = 0,
a1 = 1/0.8,
a2 = 1/0.25

To Find,
Infinite Continued Fraction Value (Cn)

Solution:
Step1: Enter a fraction value= 4 / 5 => 0.80
Step2: Value for a0 = 0
Step3: Value for a1 = 1 / 0.8 => 1.25 => 1
Step4: Value for a2 = 1 / 0.25 => 4
Step5: Combine the values obtained in step 2, 3 and 4

Infinite Continued Fraction Value Cn = [ 0 ; 1 , 4]


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