$($a$)(13$ points$)$ Convert the following number from decimal to the IEEE $32-$bit floating point. Show your work. Is this representation accurate? Explain your answer.

$-{57\mathrm{.}5}_{10}$

$($b$)(12$ points$)$ Could you convert the decimal number $421\mathrm{.}3$ into a single precision float without losing any precision from the original number? Explain your answer.