Is $\{\frac{m}{10^n}\mid m,n\in\mathbb Z,\ n\geq 0\}$ dense in $\mathbb R$?

real-analysis analysis

Hint For any $x \in \mathbb R$ we have

$$x- \frac{1}{10^n}\leq \frac{\lfloor 10^n x \rfloor}{10^n} \leq x $$


Hint: Consider the decimal representation of real numbers.

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