Consider a $($binary$)$ floating point system of the form $(1.s_1{s}_2{)}_2{2}^m$ where

min$[-31,32].$ Calculate the relative error, with respect to $1-$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.

$x=\left[\begin{array}{c}1\mathrm{.}1250000\\ 5\mathrm{.}5000000\\ 1\mathrm{.}1875000\end{array}\right]$

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 $=0\mathrm{.}001$