First of all, I think the problem was written incorrectly - I am referring to the value given for the total mass of the reactants, which I believe was 30.3 g, not 3.03 g, and to the fact that the product is zinc iodide (ZnI_2) Therefore, I'll try and make this more of a concept-problem.
So, according to the law of conservation of mass, the total mass of the reactants must be equal to the total mass of the product - mass can neither be created, nor destroyed in any ordinary chemical reaction.
Let's assume that this is the reaction we're looking for
Zn + I_2 -> ZnI_2
Since the total mass of the products is 30.3g, we know that
m_(Zn.react) + m_(I_2) = 30.3g -> this is true only for what participates in the reaction, the mass of unreacted Zn should not be included here (this is what m_(Zn.react) symbolizes).
We know that the mass of the product must equal the mass of the reactants, so
m_(ZnI_2) = m_(Zn.react) + m_(I_2) = 30.3g ->
m_(Zn.excess) = 48.12 - 30.3 = 17.8g -> excess Zn;
Knowing that we have a 1:1 mole ratio between Zn and I_2, and that their molar masses are 65.4g/(mol) and 253.8g/(mol), respectively, we can determine how much of each actually reacts:
n_(Zn.react) = n_(I_2) -> m_(Zn.react)/(65.4g/(mol)) = m_(I_2)/(253.8g/(mol)), (1) and
m_(Zn.ract) + m_(I_2) = 30.3g (2)
I won't detail the solving of this equation system because it's too simple; solving for the two masses will show that
m_(Zn.react) = 6.21g and m_(I_2) = 24.09g
Since the number of ZnI_2 moles must equal the number of Zn and I_2 moles as well, we can check the result by
n_(ZnI_2) = (30.3g)/((65.4 + 253.8)g/(mol)) = 0.0950 moles, which equals
n_(Zn.react) = (6.21g)/(65.4g/(mol)) = 0.0950 moles and
n_(I_2) = (24.09g)/(253.8g/(mol)) = 0.0950 moles.
As a conclusion, the results of this reaction agree with the law of conservation of mass: from a total of 6.21 + 17.8 = 24.01 g of Zn and 24.09 g of I_2, 30.3 g of ZnI_2 are produced ->I_2 is the limiting reagent.