Several fractions offer increasingly accurate approximations of pi (π).
According to OEIS (Online Encyclopedia of Integer Sequences) sequences A002485 and A002486, some of the initial fractions that approximate pi are:
- 3
- 22/7
- 333/106
- 355/113
- 103993/33102
- 104348/33215
The accuracy of these approximations increases with each subsequent fraction. The number of accurate decimal places for each approximation is approximately:
- 3: Good to 0 decimal places
- 22/7: Good to 2 decimal places
- 333/106: Good to 4 decimal places
- 355/113: Good to 6 decimal places
- 103993/33102: Good to 9 decimal places
- 104348/33215: Good to 9 decimal places
This can be summarized in a table:
| Fraction | Decimal Approximation | Accurate Decimal Places |
|---|---|---|
| 3 | 3.000000 | 0 |
| 22/7 | 3.142857 | 2 |
| 333/106 | 3.141509 | 4 |
| 355/113 | 3.141593 | 6 |
| 103993/33102 | 3.141592653 | 9 |
| 104348/33215 | 3.141592653 | 9 |
The fraction 355/113 is a particularly good approximation, accurate to six decimal places, and is commonly used when a reasonably precise fractional approximation is needed.
