Prove $\overline x \in [a,b]$

Question

Given $x\in [a,b]$ , round off $x$ k decimal places we have $\overline x$ . How to prove $\overline x \in [a,b]$, does it need to have more conditions? $a,b$ have $l$ digits after decimal places ($l<k$)

Answer 1

Of course more conditions are needed. Suppose that $a=x=0.1111111111\dots=\frac19$ and that $b=1$. Then $\bar x<a$ and therefore $\bar x\notin[a,b]$.