Q. Which of the following is an irrational number?Choices:(A) 9(B)β Ο(C) 0(D) 37β
Definition of Irrational Number: Understand the definition of an irrational number. An irrational number is a number that cannot be expressed as a simple fraction - that is, the ratio of two integers. It is a number that has a non-terminating, non-repeating decimal expansion.
Evaluate Choice (A): Evaluate choice (A) which is 9. The number 9 can be expressed as the fraction 19β, which is the ratio of two integers. Therefore, it is a rational number.
Evaluate Choice (B): Evaluate choice (B) which is Ο (pi).The number Ο (pi) is known to be an irrational number because it cannot be expressed as a fraction of two integers and has a non-terminating, non-repeating decimal expansion.
Evaluate Choice (C): Evaluate choice (C) which is 0. The number 0 can be expressed as the fraction 0/1, which is the ratio of two integers. Therefore, it is a rational number.
Evaluate Choice (D): Evaluate choice (D) which is 37β. The number 37β is already expressed as a fraction of two integers, which means it is a rational number.
Identify Irrational Number: Identify the irrational number from the choices.From the evaluation, we can see that choice (B) Ο is the only number that fits the definition of an irrational number.