Pi
Pi is the ratio of a circle's circumference to its diameter. Its value is 3.14159265358979323846264338327950288419716939937510…, irrational and transcendental.
How to work it out
- 1
What it is: the ratio of a circle's circumference to its diameter.
- 2
The first 100 digits, computed exactly with big-integer arithmetic:
- 3
3.14159265 3589793238 4626433832 7950288419 7169399375 1058209749 4459230781 6406286208 9986280348 2534211706 79
- 4
Its continued fraction is [3; 7; 15; 1; 292; 1; 1; 1; 2; 1, …]. Cutting it off gives the best fractions for a given size of denominator, such as 22/7, 333/106, 355/113.
How often each digit appears in the first 100 digits (computed)
| Digit | Count |
|---|---|
| 0 | 8 |
| 1 | 8 |
| 2 | 12 |
| 3 | 12 |
| 4 | 10 |
| 5 | 8 |
| 6 | 9 |
| 7 | 8 |
| 8 | 12 |
| 9 | 13 |
Best fractions from the continued fraction (computed)
| Fraction | Decimal | Error |
|---|---|---|
| 3/1 | 3.00000000000 | 1.42e-1 |
| 22/7 | 3.14285714286 | 1.26e-3 |
| 333/106 | 3.14150943396 | 8.32e-5 |
| 355/113 | 3.14159292035 | 2.67e-7 |
| 103993/33102 | 3.14159265301 | 5.78e-10 |
| 104348/33215 | 3.14159265392 | 3.32e-10 |
| 208341/66317 | 3.14159265347 | 1.22e-10 |
| 312689/99532 | 3.14159265362 | 2.91e-11 |
Questions
What is the value of Pi?
3.14159265358979323846264338327950288419716939937510…
Is Pi irrational?
It is irrational and transcendental.
What are the first 10 digits of Pi?
3.1415926535.
What is a good fraction for Pi?
22/7 is simple, and 355/113 is accurate to about 2.7e-7.