To find the change in Claire's weight, you need to subtract her weight in March from her weight in September:
\[ \text{Change in weight} = \text{Weight in September} - \text{Weight in March} \]
Substituting the given values:
\[ \text{Change in weight} = 187.4 , \text{pounds} - 163.5 , \text{pounds} \]
Calculating the difference:
\[ \text{Change in weight} = 187.4 - 163.5 = 23.9 , \text{pounds} \]
The rational number that represents the change in Claire’s weight is:
\[ \boxed{23.9} \]