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FromContinuedFraction[list]

reconstructs a number from the list of its continued fraction terms.

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FromContinuedFraction

FromContinuedFraction[list]

reconstructs a number from the list of its continued fraction terms.

Details

Examples

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Basic Examples  (1)

Wolfram Language code: ContinuedFraction[47 / 17]
Wolfram Language code: FromContinuedFraction[%]
Wolfram Language code: 2 + (1/1 + (1/3 + (1/4)))

Scope  (2)

Quadratic irrationals (recurring continued fractions):

Wolfram Language code: ContinuedFraction[Sqrt[71]]
Wolfram Language code: FromContinuedFraction[%]

Symbolic form:

Wolfram Language code: FromContinuedFraction[{a, b, c, d}]
Wolfram Language code: Together[%]

Compare with the division-based form:

Wolfram Language code: Together[a + 1 / (b + 1 / (c + 1 / d))]

Applications  (2)

Rational approximation to π:

Wolfram Language code: FromContinuedFraction[ContinuedFraction[Pi, 3]]
Wolfram Language code: N[%]

Numbers with simple recurring continued fractions:

Wolfram Language code: FromContinuedFraction[{{1}}]
Wolfram Language code: FromContinuedFraction[{{1, 2}}]
Wolfram Language code: FromContinuedFraction[{{1, 2, 3}}]
Wolfram Language code: FromContinuedFraction[{{1, 2, 3, 4}}]

Properties & Relations  (1)

Wolfram Language code: FromContinuedFraction[{x}]
Wolfram Research (1999), FromContinuedFraction, Wolfram Language function, https://reference.wolfram.com/language/ref/FromContinuedFraction.html.

Text

Wolfram Research (1999), FromContinuedFraction, Wolfram Language function, https://reference.wolfram.com/language/ref/FromContinuedFraction.html.

CMS

Wolfram Language. 1999. "FromContinuedFraction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FromContinuedFraction.html.

APA

Wolfram Language. (1999). FromContinuedFraction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FromContinuedFraction.html

BibTeX

@misc{reference.wolfram_2026_fromcontinuedfraction, author="Wolfram Research", title="{FromContinuedFraction}", year="1999", howpublished="\url{https://reference.wolfram.com/language/ref/FromContinuedFraction.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_fromcontinuedfraction, organization={Wolfram Research}, title={FromContinuedFraction}, year={1999}, url={https://reference.wolfram.com/language/ref/FromContinuedFraction.html}, note=[Accessed: 12-June-2026]}