$($a$)$ A metal rod, $1\mathrm{.}20$m long, is heated and its length expands by $42$mm$.$ Calculate the percentage increase in length. $[5$ marks$]($b$)$ The experimental temperature value at which water freezes is $275\mathrm{.}16$ K; the exact temperature is $273\mathrm{.}15$ K$.$ Find the percentage error in the experimental value. $[5$ marks$]($Note the percentage error is given by: $\%=\backslash$times $100)$