355/113 is a very accurate fractional approximation of pi (π).
Pi (π) is an irrational number, meaning it cannot be expressed exactly as a fraction of two integers. However, some fractions provide excellent approximations. One of the most famous and accurate is 355/113.
Why is 355/113 a Good Approximation?
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Accuracy: The fraction 355/113 approximates pi to about six decimal places. This is a much better approximation than simpler fractions like 22/7.
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Simplicity (Relative): While not as simple as 22/7, 355/113 is remarkably accurate considering the size of the numbers involved. It uses just six digits (three in the numerator and three in the denominator) to produce seven correct digits of π.
Comparing Approximations
Here's a comparison of some fractional approximations of pi:
| Approximation | Value | Decimal Equivalent | Accuracy (Decimal Places) |
|---|---|---|---|
| 22/7 | 3.142857... | 2 | |
| 333/106 | 3.141509... | 4 | |
| 355/113 | 3.14159292... | 6 | |
| Actual Pi | 3.14159265... | N/A |
As you can see, 355/113 provides a significant jump in accuracy compared to 22/7 and even 333/106.
In conclusion, while pi cannot be perfectly represented as a fraction, the fraction 355/113 provides a remarkably accurate approximation suitable for many practical calculations.
