8.1: Rational numbers

Definition: Rational

A real number $x$ is called a rational number if $x=\frac{m}{n}$ for some $m,n \in \mathbb{Z}, n\ne 0$.

Example $\PageIndex{1}$:

Write $2. \overline{13}$ as a fraction.

Solution

Let $x= 2. \overline{13}$. Then $100x= 213. \overline{13}$. Therefore $99 x= 211$. which implies $x=\dfrac{211}{9}$.