Allow us to contemplate

s = Round[1, 0.2] + I*Round[2, 0.3]

Round[
Complex[1., 2.], 0.36055512754639896`]

What does it imply? The documentation to the Round command says nothing about it.

Subsequent, the results of

Exp[s]

Round[-1.1312 + 2.47173 I, 0.407862 – 0.891194 I

is unclear to me in view of

NMaximize[{ComplexExpand[Re[Exp[re + I*im]]],(re-1)^2+(im-2)^2<=0.2^2+ 0.3^2},{re,im}]

{-0.184151, {re -> 0.974985, im -> 1.64031}}

Additionally

AroundReplace[Exp[re + I*im], {re -> Round[1, 0.2], im -> Round[2, 0.3]}]

Round[-1.1312 + 2.47173 I, 0.552695 + 0.252945 I]

What ought to I belief?