$($a$)$ Convert the decimal number ${13\mathrm{.}32}_{10}$ into the following notations:

i$.$ Binary notation $($up to $4$ binary points$)$

ii$.$ Octal notation $($up to $2$ octal points$)$

iii. Hexadecimal notation $($up to $1$ hexadecimal point$)$

$($b$)$ State $2$ reasons for the usage of hexadecimal notation.