Why can't pi be expressed as a fraction?

Of course pi (like every other number) can be expressed as a fraction. Indeed, as you point out it's actually defined as one -- the ratio of any circle's circumference to its diameter. read more

Of course pi (like every other number) can be expressed as a fraction. Indeed, as you point out it's actually defined as one -- the ratio of any circle's circumference to its diameter. What we can't do is express pi as the ratio of two integers. read more

If pi is the ratio of a circle's circumference to its diameter, why can't we simply take a circle, measure its circumference and diameter, and derive the read more

Pi is an irrational number, which means its exact value as a decimal number neither repeats or terminates. If you think of a fraction as just a ratio of any two numbers, then the exact value of pi is expressed as the ratio of a circle’s circumference divided by its diameter. read more