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Question

Is pi a rational or irrational number?


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Solution

Verifying whether π is a rational or an irrational number:

Rational numbers are the numbers which can be expressed in the form pq where p,q are both integers and q0.

When expressed in decimal form, rational numbers are terminating decimals or repeating in an fixed pattern

For example:

  1. 103=3.3333... is a non terminating yet repeating type of rational number.
  2. 274=6.75 is a terminating rational number.

Irrational numbers are numbers which cannot be expressed as a ratio of two integers.

When expressed in decimal form, they are non terminating and non repeating.

π is the ratio of a circle's circumference to a diameter. It is a constant value which is approximately equal to 3.14159265359.....

π is non terminating non repeating sequence of numbers and cannot be expressed as the ratio of two integers.

Hence, π is an irrational number.


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