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Which of the following is an irrational number? 1.66666666666666…, 0.02002000200002…, 0.142857142857, None of these

Which of the following is an irrational number? 1.66666666666666…, 0.02002000200002…, 0.142857142857, None of these

Explanation

Let's analyze the options:

  1. 1.66666666666666…: This is a repeating decimal, which means it's a rational number (can be expressed as a fraction, 5/3).
  2. 0.02002000200002…: This appears to be a non-repeating, non-terminating decimal, which is a characteristic of irrational numbers.
  3. 0.142857142857: This is a repeating decimal, which means it's a rational number (can be expressed as a fraction, 1/7).

Based on the analysis, the answer is 0.02002000200002….