Consider the real number $r$:$=-6543\mathrm{.}21.$ Give an upper bound on the absolute relative error and on the absolute error of the floating$-$point representation $fl(r)$ of this real number $r$ represented in a computer using IEEE double precision arithmetic, i$.$e$.,$ give upper bounds on

$|\frac{(-6543\mathrm{.}21)-fl(-6543\mathrm{.}21)}{(-6543\mathrm{.}21)}|$ and $|(-6543\mathrm{.}21)-fl(-6543\mathrm{.}21)|?$

Hint: do not try to find the binary representations of $-6543\mathrm{.}21$ and $fl(-6543\mathrm{.}21),$ but apply Lemma $1\mathrm{.}3.$