Express 8/13 as a continued fraction
In decimal terms, = 0.61538461538462
Continued Fraction Table
| Start | Integer | Decimal Portion Start - Integer | Reciprocal: 1 ÷ Decimal |
|---|---|---|---|
| 0.61538461538462 | 0 | 0.615 | 1.626 |
| 1.626 | 1 | 0.626 | 1.5974 |
| 1.5974 | 1 | 0.597 | 1.675 |
| 1.675 | 1 | 0.675 | 1.4815 |
| 1.4815 | 1 | 0.482 | 2.0747 |
| 2.0747 | 2 | 0.075 | 13.3333 |
| 13.3333 | 13 | 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 |
Stop when the difference portion = 0
Use the Integer Column
[0; 1, 1, 1, 1, 2, 13, 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?
[0; 1, 1, 1, 1, 2, 13, 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]
How does the Continued Fraction Calculator work?
Free Continued Fraction Calculator - Shows the continued fraction for a fraction
This calculator has 1 input.
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
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
- Continued Fraction 1/2
- Continued Fraction 1/3
- Continued Fraction 1/4
- Continued Fraction 1/5
- Continued Fraction 1/6
- Continued Fraction 1/7
- Continued Fraction 1/8
- Continued Fraction 1/9
- Continued Fraction 1/10
- Continued Fraction 1/11
- Continued Fraction 1/12
- Continued Fraction 1/13
- Continued Fraction 1/14
- Continued Fraction 1/15
- Continued Fraction 1/16
- Continued Fraction 2/3
- Continued Fraction 2/4
- Continued Fraction 2/5
- Continued Fraction 2/6
- Continued Fraction 2/7
- Continued Fraction 2/8
- Continued Fraction 2/9
- Continued Fraction 2/10
- Continued Fraction 2/11
- Continued Fraction 2/12
- Continued Fraction 2/13
- Continued Fraction 2/14
- Continued Fraction 2/15
- Continued Fraction 2/16
- Continued Fraction 3/4
- Continued Fraction 3/5
- Continued Fraction 3/6
- Continued Fraction 3/7
- Continued Fraction 3/8
- Continued Fraction 3/9
- Continued Fraction 3/10
- Continued Fraction 3/11
- Continued Fraction 3/12
- Continued Fraction 3/13
- Continued Fraction 3/14
- Continued Fraction 3/15
- Continued Fraction 3/16
- Continued Fraction 4/5
- Continued Fraction 4/6
- Continued Fraction 4/7
- Continued Fraction 4/8
- Continued Fraction 4/9
- Continued Fraction 4/10
- Continued Fraction 4/11
- Continued Fraction 4/12
- Continued Fraction 4/13
- Continued Fraction 4/14
- Continued Fraction 4/15
- Continued Fraction 4/16
- Continued Fraction 5/6
- Continued Fraction 5/7
- Continued Fraction 5/8
- Continued Fraction 5/9
- Continued Fraction 5/10
- Continued Fraction 5/11
- Continued Fraction 5/12
- Continued Fraction 5/13
- Continued Fraction 5/14
- Continued Fraction 5/15
- Continued Fraction 5/16
- Continued Fraction 6/7
- Continued Fraction 6/8
- Continued Fraction 6/9
- Continued Fraction 6/10
- Continued Fraction 6/11
- Continued Fraction 6/12
- Continued Fraction 6/13
- Continued Fraction 6/14
- Continued Fraction 6/15
- Continued Fraction 6/16
- Continued Fraction 7/8
- Continued Fraction 7/9
- Continued Fraction 7/10
- Continued Fraction 7/11
- Continued Fraction 7/12
- Continued Fraction 7/13
- Continued Fraction 7/14
- Continued Fraction 7/15
- Continued Fraction 7/16
- Continued Fraction 8/9
- Continued Fraction 8/10
- Continued Fraction 8/11
- Continued Fraction 8/12
- Continued Fraction 8/13
- Continued Fraction 8/14
- Continued Fraction 8/15
- Continued Fraction 8/16
- Continued Fraction 9/10
- Continued Fraction 9/11
- Continued Fraction 9/12
- Continued Fraction 9/13
- Continued Fraction 9/14
- Continued Fraction 9/15
- Continued Fraction 9/16
- Continued Fraction 10/11
- Continued Fraction 10/12
- Continued Fraction 10/13
- Continued Fraction 10/14
- Continued Fraction 10/15
- Continued Fraction 10/16
- Continued Fraction 11/12
- Continued Fraction 11/13
- Continued Fraction 11/14
- Continued Fraction 11/15
- Continued Fraction 11/16
- Continued Fraction 12/13
- Continued Fraction 12/14
- Continued Fraction 12/15
- Continued Fraction 12/16
- Continued Fraction 13/14
- Continued Fraction 13/15
- Continued Fraction 13/16
- Continued Fraction 14/15
- Continued Fraction 14/16
- Continued Fraction 15/16
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