In[1] = 10/3.
Out[1] = 0.3333
By adding a decimal point to a number, you force Mathematica to treat it as approximate. These approximate numbers will be machine precision by default. If the expression contains a decimal number,then the result is also a decimal number.
I refer to the book for more information:1.Mathematica Cookbook and 2.Mathematica Navigator
Try:
InverseZTransform[-0.9568/(z - 4.321*10^-2), z, n] // Rationalize
(* -299 2^(6 - 5 n) 5^(1 - 5 n) 4321^(-1 + n) UnitStep[-1 + n] *)
or:
InverseZTransform[-(598/625)/(z - 4321/100000), z, n]
(* -299 2^(6 - 5 n) 5^(1 - 5 n) 4321^(-1 + n) UnitStep[-1 + n] *)