$3\mathrm{.}13$ pts $[$A$]-$type error: Problems with Adding & Subtracting You want to calculate Z $=$ X$3-$ v$3$ using a fake, crappy computer that rounds numbers in the floating point format $+$ d$.$dd x $10+$d$,$ where each d is a decimal from $0-9,$ and the first d in the mantissa can't be a $0.$ There are no other rules $($don$\text{'}$t even worry about denormal or infinity, etc. this time$).$ For your example, assume X $=12\mathrm{.}5$ and Y $=12\mathrm{.}4.($a$)$ Calculate the computer's value for Z the "standard" way: first cubing X $($and rounding the answer back to a storable value$),$ then cubing Y $($and rounding the answer back to a storable value$),$ then subtracting the two $($and rounding that back to a storable value$).$ Show me all your work! $($b$)$ What is the percent error in the calculation from $($a$)?($c$)$ Describe for me a better way of calculating Z on this $($fake$,$ crappy$)$ computer, and compare the percent error in your improved calculation with that from $($a$).$ Be sure to still follow all the computer rules $-$ showing me how the computer does each individual calculation and rounding the answer back to a storable value before moving on to the next step! Hint: X$3$ y$\}=($X$-$Y$)*($x$2+$XY$+$Y$2)$