Question

Determine if 0, point, 8, 3, 8, 7, 6, 6, 7, 6, 8, 8, 3, 8, 6, 7, 5, 9, dot dot dot0.8387667688386759... is rational or irrational and give a reason for your answer.
Answer

The number 0, point, 8, 3, 8, 7, 6, 6, 7, 6, 8, 8, 3, 8, 6, 7, 5, 9, dot dot dot0.8387667688386759... is
because it is a decimal that terminates
it is the square root of a perfect square
it is a decimal that repeats
it is a decimal that does not repeat or terminate
it is the square root of a non-perfect square

Answer 1

The number 0.8387667688386759... is **irrational** because it is a decimal that does not repeat or terminate.

Rational numbers can be expressed as a fraction of two integers and include both terminating and repeating decimals. However, since this decimal goes on indefinitely without repeating a pattern, it cannot be expressed as a fraction of two integers, making it irrational.