The populations of three states are A: $1300 ; B: 6280 ; C: 230$. Determine how 100 delegates should be apportioned among these states using Hamilton's method. Then suppose that a new state with a population of 400 is added to the system, along with 8 new seats. Determine the apportionment for the four states (assuming the populations of the first three states remain the same). Does the addition of the new state decrease the representation of any of the original states?

Fill in the table for the initial final apportionment for the three states.
\begin{tabular}{l|ccc}
State & A & B & C \\
\hline Final Apportionment & $\square$ & $\square$ & $\square$
\end{tabular}

Step 1 ：Calculate the total population of the three states, which is \(1300 + 6280 + 230 = 7810\).

Step 2 ：Calculate the standard divisor by dividing the total population by the number of delegates, which is \(7810 \div 100 = 78.1\).

Step 3 ：Calculate the standard quota for each state by dividing the population of each state by the standard divisor. The standard quotas are \(1300 \div 78.1 = 16.645326504481435\) for state A, \(6280 \div 78.1 = 78.40973111395647\) for state B, and \(230 \div 78.1 = 2.9449423815621\) for state C.

Step 4 ：The final apportionment for each state is the integer part of the standard quota, which is \(\boxed{16}\) for state A, \(\boxed{82}\) for state B, and \(\boxed{2}\) for state C.

Step 5 ：Calculate the total population of the four states, which is \(1300 + 6280 + 230 + 400 = 8210\).

Step 6 ：Calculate the standard divisor by dividing the total population by the number of delegates, which is \(8210 \div 108 = 76.01851851851852\).

Step 7 ：Calculate the standard quota for each state by dividing the population of each state by the standard divisor. The standard quotas are \(1300 \div 76.01851851851852 = 17.10109622411693\) for state A, \(6280 \div 76.01851851851852 = 81.61144945188794\) for state B, \(230 \div 76.01851851851852 = 3.02557856272838\) for state C, and \(400 \div 76.01851851851852 = 5.261875761266748\) for the new state.

Step 8 ：The final apportionment for each state is the integer part of the standard quota, which is \(\boxed{17}\) for state A, \(\boxed{83}\) for state B, \(\boxed{3}\) for state C, and \(\boxed{5}\) for the new state.

Step 9 ：Comparing the final apportionment of the original three states in the two scenarios, we can see that the representation of state A increases by 1, the representation of state B increases by 1, and the representation of state C increases by 1. Therefore, the addition of the new state does not decrease the representation of any of the original states.