To find the change in Claire's weight, we subtract her weight in March from her weight in September.
September weight: 187.4 pounds
March weight: 163.5 pounds
Change in weight = September weight - March weight
Change in weight = 187.4 - 163.5 = 23.9 pounds
So, the rational number representing the change in Claire's weight is \( -23.9 \) pounds, indicating a loss of 23.9 pounds.