Continued Fraction for 4/15



Express 4/15 as a continued fraction

In decimal terms, = 0.67
Start NumberInteger NumberDecimal Portion = Start - IntegerReciprocal =1 ÷ Decimal Portion
0.6700.2673.7453
3.745330.7451.3423
1.342310.3422.924
2.92420.9241.0823
1.082310.08212.1951
12.1951120.1955.1282
5.128250.1287.8125
7.812570.8131.23
1.2310.234.3478
4.347840.3482.8736
2.873620.8741.1442
1.144210.1446.9444
6.944460.9441.0593
1.059310.05916.9492
16.9492160.9491.0537
1.053710.05418.5185
18.5185180.5191.9268
1.926810.9271.0787
1.078710.07912.6582
12.6582120.6581.5198
1.519810.521.9231
1.923110.9231.0834
1.083410.08312.0482
12.0482120.04820.8333
20.8333200.8331.2005
1.200510.2014.9751
4.975140.9751.0256
1.025610.02638.4615
38.4615380.4622.1645
2.164520.1656.0606
6.060660.06116.3934
16.3934160.3932.5445
2.544520.5451.8349
1.834910.8351.1976
1.197610.1985.0505
5.050550.05119.6078
19.6078190.6081.6447
1.644710.6451.5504
1.550410.551.8182
1.818210.8181.2225
1.222510.2234.4843
4.484340.4842.0661
2.066120.06615.1515
15.1515150.1526.5789
6.578960.5791.7271
1.727110.7271.3755
1.375510.3762.6596
2.659620.661.5152
1.515210.5151.9417
1.941710.9421.0616
1.061610.06216.129
16.129160.1297.7519
7.751970.7521.3298
1.329810.333.0303
3.030330.0333.3333
33.3333330.3333.003
3.00330.003333.3333
333.33333330.3333.003
3.00330.003333.3333
333.33333330.3333.003
3.00330.003333.3333
333.33333330.3333.003
3.00330.003333.3333
333.33333330.3333.003
3.00330.003333.3333
333.33333330.3333.003
3.00330.003333.3333
333.33333330.3333.003
3.00330.003333.3333
333.33333330.3333.003
3.00330.003333.3333
333.33333330.3333.003
3.00330.003333.3333
333.33333330.3333.003
3.00330.003333.3333
333.33333330.3333.003
3.00330.003333.3333
333.33333330.3333.003
3.00330.003333.3333
333.33333330.3333.003
3.00330.003333.3333
333.33333330.3333.003
3.00330.003333.3333
333.33333330.3333.003
3.00330.003333.3333
333.33333330.3333.003
3.00330.003333.3333
333.33333330.3333.003
3.00330.003333.3333
333.33333330.3333.003
3.00330.003333.3333
333.33333330.3333.003
3.00330.003333.3333
333.33333330.3333.003
3.00330.003333.3333
333.33333330.3333.003
3.00330.003333.3333
333.33333330.3333.003
3.00330.003333.3333
333.33333330.3333.003

We stop when the difference portion = 0, and use the Integer Column for our representation:
Our continued fraction representation is: [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]