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Which of the following is an irrational number?\newlineChoices:\newline(A) 99\newline(B)​ Ο€\pi\newline(C) 00\newline(D) 73\frac{7}{3}

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Q. Which of the following is an irrational number?\newlineChoices:\newline(A) 99\newline(B)​ Ο€\pi\newline(C) 00\newline(D) 73\frac{7}{3}
  1. 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.
  2. Evaluate Choice (A): Evaluate choice (A) which is 99. The number 99 can be expressed as the fraction 91\frac{9}{1}, which is the ratio of two integers. Therefore, it is a rational number.
  3. Evaluate Choice (B): Evaluate choice (B) which is Ο€\pi (pi).\newlineThe number Ο€\pi (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.
  4. Evaluate Choice (C): Evaluate choice (C) which is 00. The number 00 can be expressed as the fraction 0/10/1, which is the ratio of two integers. Therefore, it is a rational number.
  5. Evaluate Choice (D): Evaluate choice (D) which is 73\frac{7}{3}. The number 73\frac{7}{3} is already expressed as a fraction of two integers, which means it is a rational number.
  6. Identify Irrational Number: Identify the irrational number from the choices.\newlineFrom the evaluation, we can see that choice (B) Ο€\pi is the only number that fits the definition of an irrational number.

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