Question

determine if 0.9584584584584584... is rational or irrational and give a rea answer.

answer attempt 1 out of 2

the number 0.9584584584584584... is because
irrational
rational
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Explanation:

Step1: Recall rational number definition

A rational number is a number that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q
eq0$. Repeating decimals are rational because they can be converted to fractions.

Step2: Analyze the decimal

The decimal $0.9584584584584584...$ has a repeating pattern "584" (after the initial "9"). Repeating decimals are rational as they can be represented as a fraction.

Answer:

rational (because it is a repeating decimal, and repeating decimals can be expressed as a fraction of two integers)