Express 4/15 as a continued fraction
In decimal terms, = 0.26666666666667
Continued Fraction Table
| Start | Integer | Decimal Portion Start - Integer | Reciprocal: 1 ÷ Decimal |
|---|---|---|---|
| 0.26666666666667 | 0 | 0.267 | 3.7453 |
| 3.7453 | 3 | 0.745 | 1.3423 |
| 1.3423 | 1 | 0.342 | 2.924 |
| 2.924 | 2 | 0.924 | 1.0823 |
| 1.0823 | 1 | 0.082 | 12.1951 |
| 12.1951 | 12 | 0.195 | 5.1282 |
| 5.1282 | 5 | 0.128 | 7.8125 |
| 7.8125 | 7 | 0.813 | 1.23 |
| 1.23 | 1 | 0.23 | 4.3478 |
| 4.3478 | 4 | 0.348 | 2.8736 |
| 2.8736 | 2 | 0.874 | 1.1442 |
| 1.1442 | 1 | 0.144 | 6.9444 |
| 6.9444 | 6 | 0.944 | 1.0593 |
| 1.0593 | 1 | 0.059 | 16.9492 |
| 16.9492 | 16 | 0.949 | 1.0537 |
| 1.0537 | 1 | 0.054 | 18.5185 |
| 18.5185 | 18 | 0.519 | 1.9268 |
| 1.9268 | 1 | 0.927 | 1.0787 |
| 1.0787 | 1 | 0.079 | 12.6582 |
| 12.6582 | 12 | 0.658 | 1.5198 |
| 1.5198 | 1 | 0.52 | 1.9231 |
| 1.9231 | 1 | 0.923 | 1.0834 |
| 1.0834 | 1 | 0.083 | 12.0482 |
| 12.0482 | 12 | 0.048 | 20.8333 |
| 20.8333 | 20 | 0.833 | 1.2005 |
| 1.2005 | 1 | 0.201 | 4.9751 |
| 4.9751 | 4 | 0.975 | 1.0256 |
| 1.0256 | 1 | 0.026 | 38.4615 |
| 38.4615 | 38 | 0.462 | 2.1645 |
| 2.1645 | 2 | 0.165 | 6.0606 |
| 6.0606 | 6 | 0.061 | 16.3934 |
| 16.3934 | 16 | 0.393 | 2.5445 |
| 2.5445 | 2 | 0.545 | 1.8349 |
| 1.8349 | 1 | 0.835 | 1.1976 |
| 1.1976 | 1 | 0.198 | 5.0505 |
| 5.0505 | 5 | 0.051 | 19.6078 |
| 19.6078 | 19 | 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 |
Stop when the difference portion = 0
Use the Integer Column
[0; 3, 1, 2, 1, 12, 5, 7, 1, 4, 2, 1, 6, 1, 16, 1, 18, 1, 1, 12, 1, 1, 1, 12, 20, 1, 4, 1, 38, 2, 6, 16, 2, 1, 1, 5, 19, 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]
