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Share-Based Payments (Narrative) (Details) - USD ($)
$ / shares in Units, shares in Millions, $ in Millions
12 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Maximum number of shares authorized for issuance (in shares) 14.9    
Shares available for future awards (in shares) 2.6    
Share-based compensation expense $ 23.9 $ 27.3 $ 19.2
Tax benefit recognized for share-based compensation arrangements $ 5.7 $ 6.6 $ 4.6
Share options granted (in shares) 0.3    
RSE awards      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Anti-dilutive awards excluded from the calculation of diluted weighted-average shares outstanding (in shares) 0.2 0.0 0.1
Share options      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Vesting period (in years) 3 years    
Expiration period (in years) 10 years    
Share options granted (in shares) 0.3 0.2  
Compensation expense to be recognized over vesting period $ 4.6 $ 3.1  
Unrecognized compensation expense, share options $ 4.4    
Unrecognized compensation expense, weighted-average period to recognize (in years) 1 year 6 months    
PSU awards      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Unrecognized compensation expense, weighted-average period to recognize (in years) 2 years 9 months 18 days    
Unrecognized compensation expense, RSE awards $ 7.8    
Weighted-average grant date fair value, granted (in usd per share) $ 63.75 $ 56.53 $ 29.25
Estimated fair value of vested awards $ 12.5    
RSE awards      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Unrecognized compensation expense, weighted-average period to recognize (in years) 2 years 2 months 12 days    
Unrecognized compensation expense, RSE awards $ 24.9    
Weighted-average grant date fair value, granted (in usd per share) $ 42.49 $ 35.16 $ 29.25
Estimated fair value of vested awards $ 15.4 $ 13.2 $ 11.5