Question

Determine if 0, point, 3, 9, 3, 9, 9, 3, 9, 9, 9, 3, 9, 9, 9, 9, 3, 9, 9, 9, 9, 9, 3, dot dot dot0.393993999399993999993... is rational or irrational and give a reason for your answer.
Answer
Attempt 1 out of 5

The number 0, point, 3, 9, 3, 9, 9, 3, 9, 9, 9, 3, 9, 9, 9, 9, 3, 9, 9, 9, 9, 9, 3, dot dot dot0.393993999399993999993... is
because ( it is a decimal that does not repeat or terminate , it is the square root of a non-perfect square , it is the square root of a perfect square , it is a decimal that repeats , it is a decimal that terminates. )

Answer 1

The number 0.393999399939999399993... is irrational because it is a decimal that does not repeat or terminate.

The sequence of digits appears to have a pattern at first (with the number 3 repeating periodically), but the presence of the infinite sequence of 9's as well as the fact that it does not settle into a fixed repeating block means it does not represent a rational number, which would either terminate or repeat after a certain point.