Continued Fraction
Expand a number and its best rational approximations
[3; 7, 15, 1, 292, 1, 1, 1, …]
Continued fraction
[3; 7, 15, 1, 292, 1, 1, 1, …]
As a fraction
3141592653589793 / 1000000000000000
Value
3,1415926536
Convergents (best rational approximations)
| k | pₖ / qₖ | Decimal | Error |
|---|---|---|---|
| 0 | 3/1 | 3 | 0,142 |
| 1 | 22/7 | 3,1428571429 | 0,00126 |
| 2 | 333/106 | 3,141509434 | 0,0000832 |
| 3 | 355/113 | 3,1415929204 | 0,000000267 |
| 4 | 103993/33102 | 3,141592653 | 0,000000000578 |
| 5 | 104348/33215 | 3,1415926539 | 0,000000000332 |
| 6 | 208341/66317 | 3,1415926535 | 0,000000000122 |
| 7 | 312689/99532 | 3,1415926536 | 0,0000000000291 |
Truncated: the number has more terms than shown. Raise the term count to see more.