Question

jordan says that $pi$ and $0.overline{3}$ are both irrational numbers. identify the mistake and name the correct classification for $0.overline{3}$. $0.overline{3}$ is a number

Explanation:

Step1: Recall number - type definitions

An irrational number cannot be written as a fraction $\frac{a}{b}$ where $a,b$ are integers and $b
eq0$. A rational number can be written as such a fraction.

Step2: Express $0.\overline{3}$ as a fraction

Let $x = 0.\overline{3}=0.333\cdots$. Then $10x=3.333\cdots$. Subtracting $x$ from $10x$ gives $10x - x=3.333\cdots - 0.333\cdots$, so $9x = 3$, and $x=\frac{1}{3}$.

Answer:

rational