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Continued Fractions

Tool to compute continued fractions. A continued fraction is the representation of a number N in a form of a series of integers (a0, a1, ..., an) such as N = (a0+1/(a1+1/(a2+1/(...1/(an))).

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Continued Fractions -

Tag(s) : Mathematics

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# Continued Fractions

## Continued Fraction Calculator

Tool to compute continued fractions. A continued fraction is the representation of a number N in a form of a series of integers (a0, a1, ..., an) such as N = (a0+1/(a1+1/(a2+1/(...1/(an))).

### How to calculate a continued fraction?

Continued fraction expansion is close to algorithm of euclidean division, as for PGCD.

Consider the fraction $$355/113 = 3.14159292035...$$ $$355 = 3 \times 113 + 16 \\ 113 = 7 \times 16 + 1 \\ 16 = 16 \times 1 + 0$$

Example: The continued fraction is [3,7,16]

### How to calculate the continued fraction of a root?

Calculate an approximate value of the root (as accurate as possible) and dCode will provide the corresponding continuous fraction.