Consider a $($binary$)$ floating point system of the form $(1.s_1{s}_2{)}_2{2}^m$ where min$[-15,16].$ Calculate the relative error, with

respect to $2-$norm if we convert the vector $n{R}^3$ to the given floating point system. When converting to floating point, first

convert to a binary number then truncate any additional bits.

$x=\left[\begin{array}{c}7\mathrm{.}5000000\\ 1\mathrm{.}2500000\\ 1\mathrm{.}1875000\end{array}\right]$

Note: We are interested in the representation accuracy of floating point. So assume that all operations performed $($addition$,$

subtraction, etc.$)$ do not increase the error.

relative error$(x)=,$ number $($ rtol $=0\mathrm{.}01,$ atol $=0\mathrm{.}001)$