Rounding Error Analysis is routinely used to compute a worst-case error bound on the result of algorithms that use floating-point arithmetic. However, for some applications (e.g., when it is necessary to prove some inclusion of the result in a domain), the knowledge of both an upper-bound of the magnitude of the error and of its sign is paramount. Using standard rounding error analysis together with a simple systematic approach, we compute such information for the expressions $3x$, $x/3$, $3(x/3)$, and $3x/3$, which can be used, e.g., in the proof of interval arithmetic operators.