Question

Determine if 0, point, 2, 7, 3, 2, 2, 3, 7, 0, 0, 1, 3, 4, 1, 4, dot dot dot0.27322370013414... is rational or irrational and give a reason for your answer.
Answer
Attempt 2 out of 2

The number 0, point, 2, 7, 3, 2, 2, 3, 7, 0, 0, 1, 3, 4, 1, 4, dot dot dot0.27322370013414... is
rational
because
it is a decimal that does not repeat or terminate

Submit Answer

Answer 1

Irrational.

Rationale: A real number is rational exactly when its decimal expansion either terminates or eventually repeats a fixed block of digits. The given expansion 0.27322370013414… is presented as non-terminating and non-repeating, so it cannot be rational; therefore it is irrational.