$($a$).$ A $30-m$ steel tape, known to be $30\mathrm{.}004$ m $($under standard conditions$),$ was used to record a measurement of $129\mathrm{.}085$ m $.$ What is the distance corrected for the erroneous tape length?

$[15]$

$($b$).$ A $100-$ft steel tape known to be only $99\mathrm{.}98$ ft long $($under standard conditions$)$ was used to record a measurement of $276\mathrm{.}22ft.$ What is the distance corrected for the erroneous tape?

$[10]$