and deduce that $0\mathrm{.}1$ has the base $2$ representation $\frac{0\mathrm{.}000}{b}ar(1100)($repeating last $4$ bits$).$ Let tilde$(x)=fl(0\mathrm{.}1)$

be the rounded version of $x=0\mathrm{.}1$ obtained in binary IEEE single precision arithmetic $(=2^{-24}).$

Show that

$\frac{x-(tilde(x))}{x}=-\frac{1}{4}.(see$ the screenshot$)$