Question

question determine if 0.393993999399993999993... is rational or irrational and give a reason for your answer. answer attempt 1 out of 5 the number 0.393993999399993999993... is irrational because it is a decimal that repeats it is the square root of a non - perfect square it is the square root of a perfect square it is a decimal that does not repeat or terminate it is a decimal that terminates

Explanation:

Step1: Recall rational - irrational definitions

Rational numbers can be written as a fraction $\frac{p}{q}$ ($q
eq0$) and have either terminating or repeating decimal expansions. Irrational numbers have non - repeating and non - terminating decimal expansions.

Step2: Analyze the given number

The number $0.393993999399993999993\ldots$ has a non - repeating pattern of digits after the decimal point. It does not have a fixed block of digits that repeat over and over again, nor does it terminate.

Answer:

The number $0.393993999399993999993\ldots$ is irrational because it is a decimal that does not repeat or terminate.