Suppose you have an approximation ${\displaystyle M}$ for a certain quantity, with a lower bound on the error of ${\displaystyle \alpha }$ and an upper bound of ${\displaystyle \beta }$. Then, the true value lies somewhere in between ${\displaystyle M+\alpha }$ and ${\displaystyle M+\beta }$. We can centre the error by picking the midpoint, ${\displaystyle M+{\frac {\beta +\alpha }{2}}}$; now our error is ${\displaystyle \pm {\frac {\beta -\alpha }{2}}}$. Therefore, the approximation can be written as ${\displaystyle \left(M+{\frac {\beta +\alpha }{2}}\right)\pm {\frac {\beta -\alpha }{2}}}$.