Continued Fraction for 9/13

Express 9/13 as a continued fraction

In decimal terms, = 0.69230769230769

Start Number	Integer Number	Decimal Portion = Start - Integer	Reciprocal =1 ÷ Decimal Portion
0.69230769230769	0	0.692	1.4451
1.4451	1	0.445	2.2472
2.2472	2	0.247	4.0486
4.0486	4	0.049	20.4082
20.4082	20	0.408	2.451
2.451	2	0.451	2.2173
2.2173	2	0.217	4.6083
4.6083	4	0.608	1.6447
1.6447	1	0.645	1.5504
1.5504	1	0.55	1.8182
1.8182	1	0.818	1.2225
1.2225	1	0.223	4.4843
4.4843	4	0.484	2.0661
2.0661	2	0.066	15.1515
15.1515	15	0.152	6.5789
6.5789	6	0.579	1.7271
1.7271	1	0.727	1.3755
1.3755	1	0.376	2.6596
2.6596	2	0.66	1.5152
1.5152	1	0.515	1.9417
1.9417	1	0.942	1.0616
1.0616	1	0.062	16.129
16.129	16	0.129	7.7519
7.7519	7	0.752	1.3298
1.3298	1	0.33	3.0303
3.0303	3	0.03	33.3333
33.3333	33	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, 2, 4, 20, 2, 2, 4, 1, 1, 1, 1, 4, 2, 15, 6, 1, 1, 2, 1, 1, 1, 16, 7, 1, 3, 33, 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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