It represents different ratios in a circle. You should be familiar with the following dimensions of a circle: For any circle, pi represents the following ratios: Pi does not have a fixed value. Any real number that is not rational is defined as an irrational number. Pi is an irrational number. Even between a single pair of rational numbers … Pi, or π, is defined as the ratio of the circumference of a circle to its diameter.Pi is an irrational number, meaning it cannot be written as a … Mathematicians have proved that certain special numbers are irrational, for example Pi and e. The number e is the base of natural logarithms. So in essence, it cannot be expressed as the ratio of two integers that have no other common factor other than one. In fact, there is what mathematicians call an uncountably infinite number of irrational numbers. No irrational number can be expressed by a rational number, even in decimal form, because decimal form is another way of writing a rational number. I have read that if circumference can be expressed as an integer then diameter cannot and vice-versa, so that the ratio can never be expressed as a/b where both a,b are integers & hence Pi is irrational. Irrational numbers aren’t rare, though. The simple answer is ‘pi’ is not equal to 22/ 7 or circumference / diameter. Famous examples of irrational numbers are √2, the constant e = 2.71828…., and the constant π = 3.14159… While it might seem intuitive or obvious that π is an irrational number, I was always curious how you would go about proving π is an irrational number. Rational numbers are of the form a / b ( a, b integers, b ≠ 0 ). Pi = C / D (circumference / diameter) . It is represented by the symbol . The fact is, “22/ 7 or circumference / diameter” is the NEAREST RATIONAL NUMBER to that irrational number. For example, Niven also proved that the cosine of a rational number is irrational. Well, this is actually just an approximation. 22/7 is 3.142; whereas pi is 3.1415—the value differs at only the third digit! Pi is an example of a irrational number. Irrational. Yes, there’s a number called ‘e’, but it’s also known as Euler’s Number. Then, why 22/7 you ask? Like all irrational numbers, π cannot be represented as a common fraction (also known as a simple or vulgar fraction), by the very definition of irrational number (i.e., not a rational number).But every irrational number, including π, can be represented by an infinite series of nested fractions, called a continued fraction: = + + + + + + + + ⋱ Truncating the continued … If now \(\pi\) were rational, \(\cos \pi = −1\) would be irrational. Rational numbers can be written in quotient form (a/b, b!=0) where a and b are integers, but since the digits in pi (pi) never end and never recur, there are no numbers to which is can be simplified that would allow for it to be written as a fraction. List 6 – Special Numbers: Pi, Euler’s number, Golden Ratio; These lists are not exclusive but do provide a way to create irrational numbers. Therefore it is an irrational number. Irrational Number – Definition.