Continued Fraction for 10/13

Express 10/13 as a continued fraction

In decimal terms, = 0.76923076923077

Start Number	Integer Number	Decimal Portion = Start - Integer	Reciprocal =1 ÷ Decimal Portion
0.76923076923077	0	0.769	1.3004
1.3004	1	0.3	3.3333
3.3333	3	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333
333.3333	333	0.333	3.003
3.003	3	0.003	333.3333

We stop when the difference portion = 0, and use the Integer Column for our representation:

Our continued fraction representation is: [0; 1, 3, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3, 333, 3]

What is the Answer?

How does the Continued Fraction Calculator work?

Shows the continued fraction for a fraction
This calculator has 1 input.

What 2 formulas are used for the Continued Fraction Calculator?

Decimal Portion = Start - Integer
Reciprocal = 1 / Decimal Portion

For more math formulas, check out our Formula Dossier

What 4 concepts are covered in the Continued Fraction Calculator?

continued fraction: a fraction whose numerator is an integer and whose denominator is an integer plus a fraction whose numerator is an integer and whose denominator is an integer plus a fraction and so on
decimal: Number in the form a/b where the result is not a whole number
fraction: how many parts of a certain size exist
a/b where a is the numerator and b is the denominator
integer: a whole number; a number that is not a fraction
...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...

Example calculations for the Continued Fraction Calculator

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