Maybe you could use rounding and $MachineEpsilon to get rid of the trailing zeros:
a = {1.000000000000000000, 2.000000000000000000}; (*this is the position*)
b = {1.456783454656574576, 4.546562323253456534}; (*value at that position*)
c = Round[#, $MachineEpsilon] & /@ Transpose[{a, b}]
{{1., 1.45678}, {2., 4.54656}}
FortranForm@c
List(List(1.,1.4567834546565746),List(2.,4.546562323253457))
$MachineEpsilon
2.22045*10^-16