I have a question, if $\displaystyle \{q_{n}\}_{n=1}^{\infty}$ is a sequence of all rational numbers, let $\displaystyle I_{n}=[q_{n}-\frac{1}{10^{n}},q_{n}+\frac{1}{10^{n}}]$

why do we have the following inclusion $\displaystyle \mahbb{Q}\subset \displaystyle\cup_{n=1}^{\infty}I_{n}$?