How to Calculate Continued Fraction
What is Continued Fraction?
Continued fractions express numbers as nested fractions: x = a₀ + 1/(a₁ + 1/(a₂ + ...)); useful for rational approximations.
Step-by-Step Guide
- 1Input decimal or fraction
- 2Generate continued fraction expansion
- 3Calculate convergents (increasingly accurate approximations)
Worked Examples
Input
Pi ≈ 3.14159
Result
CF = [3; 7, 15, 1, 292, ...], convergent 355/113 ≈ 3.14159 (extremely accurate)
Common Mistakes to Avoid
- ✕Terminating before accurate enough
- ✕Confusing with decimal fractions
Frequently Asked Questions
Why continued fractions?
Best rational approximations; pi convergents used in engineering.
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