  Lower and upper bounds $B_a(x)$ on the incomplete gamma function
$\Gamma(a,x)$ are given for all real $a$ and all real $x>0$. These bounds
$B_a(x)$ are exact in the sense that
$B_a(x)\underset{x\downarrow0}\sim\Gamma(a,x)$ and
$B_a(x)\underset{x\to\infty}\sim\Gamma(a,x)$. Moreover, the relative errors of
these bounds are rather small for other values of $x$, away from $0$ and
$\infty$.
