is pi a rational number?

Question

if pi is the ratio of a circle's circumference to diameter, then why is it not considered rational?

Answer 1

A rational number must be a ratio of two integers.

If a circle's diameter is an integer, then it's circumference is not, and vice versa.

Answer 2

Pi is a "proportionality constant" designed to compensate for the theory that the diameter and radius of one circle will never both be integers. It is not Pi that is not rational, because the constant Pi itself is not a proportion. What's irrational is the ratio of diameter to circumference of all circles because to date, a circle large enough to have integer diameter and circumference has not yet been determined. If and when one is calculated, the whole world will soon know.

Answer 3

A rational number is defined to be a number that can be expressed as the quotient of two integers. Because the circumferance and diameter of a circle are not both integers, then pi is not a rational number.

In other words, because pi can not be put into a fraction of integers, it is irrational.

Answer 4

Any value that can be represented as a repeating decimal fraction is rational. This includes decimals that terminate because .35 can be thought of as .3500000000000... where the zero repeats forever. PI is not representable as a repeating fraction, so indeed it is irrational. Other irrational numbers include the positive square root of 2. But PI goes even beyond that. The square root of two is a root of the algebraic equation x^2 = 2. PI is not the root of any algebraic equation of any sort. It is a non-algebraic number which makes it transcendental.

Answer 5

Because you need a ratio of integers. If the diameter is an integer the circumference is not, and vice versa.

So pi is irrational. It cannot be expressed as a ratio of integers but instead is a series of non-repeating decimals.

pi is one of infinitely many irrational numbers (such as sqrt(2), e, phi, etc.)

Answer 6

In other words, no. A non repeating, non terminating decimal value is always an irrational number.

Answer 7

Pie is likely not rational because of the varying degrees of filling that one can choose. Because of these seemingly infinite and indeterminate variable fillings, Pie is probably one of the most irrational desserts you could ever prepare!

Answer 8

no. its not rational because the number sequences never repeat