No fraction exactly equals pi (π). Pi is an irrational number, meaning it cannot be expressed as a ratio of two integers.
Why Pi Can't Be Represented as a Fraction
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Irrational Numbers: Irrational numbers have decimal representations that are non-repeating and non-terminating. This fundamentally prevents them from being written as a simple fraction.
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Definition of a Fraction: A fraction, by definition, is a ratio of two integers (whole numbers).
Approximations of Pi as Fractions
While pi cannot be exactly represented as a fraction, several fractions are commonly used to approximate its value. These approximations are useful in various calculations and applications.
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22/7: This is a common and easily remembered approximation. It is accurate to about two decimal places (3.14).
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355/113: This is a more accurate approximation, accurate to about six decimal places (3.141593).
Comparison of Pi and Its Approximations
| Value | Decimal Representation | Accuracy |
|---|---|---|
| Pi (π) | 3.1415926535... | Exact Value |
| 22/7 | 3.1428571428... | Approximate (2 decimal places) |
| 355/113 | 3.1415929203... | Approximate (6 decimal places) |
Conclusion
In conclusion, while numerous fractions can approximate pi to varying degrees of accuracy, no fraction can represent the exact value of pi because pi is an irrational number.
