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.