Continued Fraction Calculator
Decimal to Continued Fraction
Convert a decimal number to its continued fraction representation
Fraction to Continued Fraction
Convert a fraction (numerator/denominator) to continued fraction form
Formula
x = a₀ + 1/(a₁ + 1/(a₂ + 1/(a₃ + ...))) | Notation: [a₀; a₁, a₂, a₃, ...]
Frequently Asked Questions
What is a continued fraction?
A continued fraction represents a number as a sequence of integer quotients: a₀ + 1/(a₁ + 1/(a₂ + ...)). Written as [a₀; a₁, a₂, ...]. For example, the golden ratio φ = [1; 1, 1, 1, ...] and π ≈ [3; 7, 15, 1, 292, ...].
What are convergents?
Convergents are the rational numbers obtained by truncating a continued fraction at each step. They provide the best rational approximations for a given denominator size. For example, 22/7 and 355/113 are famous convergents of π.
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