is it true that for every real number x there is a sequence of rationals (of the form m/2^n) that converges to x ??

Question

Is it true that for every real number $x$ there is a sequence of rationals of the form ($m/2^n$) that converges to $x$ ?

where ($m/2^n$) is in base 10 , $m,n\in N$ .

Answer 1

HINT: For every $n$ there exists $m$ such that $x\in\left[\frac{m}{2^n},\frac{m+1}{2^n}\right)$.