deduce that $\mathbb{Q}$ and $\mathbb{D}$ are dense

Question

i have a question

let $b \geq 2$ and for $n$ a natural number

$Q_n = \Bigg\{ \frac{k}{b^n} ,k\in \mathbb{N} , 0 \leq k < b^n \Bigg\} $

i have proved for all real number in $[0,1]$. there exists $r_n \in Q_n$

such that $r_n \leq x < r_n + \frac{1}{b^n} $

how to deduce that the set of rational numbers $\mathbb{Q}$ the decimal numbers $\mathbb{D}$ are dense in $\mathbb{R}$

please help me with this question with some hints