When switch $\backslash ($ S $\backslash )$ in the figure is open, the voltmeter V of the battery reads $3\mathrm{.}05$ V $.$ When the switch is closed, the voltmeter reading drops to $2\mathrm{.}98$ V $,$ and the ammeter A reads $1\mathrm{.}63$ A $.$ Assume that the two meters are ideal, so they do not affect the circuit. $($Figure $1)$

Part A

Find the emf $\backslash (\backslash$mathcal$\{$E$\}\backslash ).$

Express your answer in volts to three significant digits.

$\backslash (\backslash$square $\backslash )$