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Share-Based Compensation (Narrative) (Details)
$ / shares in Units, $ in Millions
12 Months Ended
Sep. 30, 2017
USD ($)
$ / shares
shares
Sep. 30, 2016
USD ($)
$ / shares
shares
Sep. 30, 2015
USD ($)
$ / shares
Oct. 03, 2016
$ / shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Shares available for future grant | shares 4,922,382      
Closing stock price (in dollars per share) | $ / shares $ 151.22 $ 150.35   $ 140.38
Conversion ratio for separation adjustments 1.071      
Cash received from option exercises $ 68.4 $ 141.3 $ 121.3  
Deferred Stock Units        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Number of units/shares granted | shares 283,000      
Weighted-average grant date fair value (in dollars per share) | $ / shares $ 148.89      
Cash payments made for deferred stock units $ 2.1 2.9 9.6  
Unrecognized compensation costs $ 39.0      
Unrecognized compensation costs, period for recognition, years 2 years      
Fair value of deferred stock units paid $ 36.6 $ 41.6 $ 35.5  
Deferred Stock Units | Minimum        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting or deferral Period 2 years      
Deferred Stock Units | Maximum        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting or deferral Period 5 years      
Director Deferred Stock Units | Maximum        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Period after service in which to elect payment 10 years      
Market-Based Deferred Stock Unit        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting or deferral Period 3 years      
Number of units/shares granted | shares 117,692 130,167    
Weighted-average grant date fair value (in dollars per share) | $ / shares $ 156.87 $ 135.49    
Time-Based Deferred Stock Unit        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Number of units/shares granted | shares 165,120.792160577      
Weighted-average grant date fair value (in dollars per share) | $ / shares $ 143.75      
Stock Options        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting or deferral Period 3 years      
Unrecognized compensation costs $ 0.1      
Unrecognized compensation costs, period for recognition, years 2 months      
Exercisable period from grant date 10 years      
Weighted-average grant date fair value of stock option (in dollars per share) | $ / shares     $ 37.19  
Intrinsic value of stock options exercised $ 57.3 $ 115.3 $ 115.5  
Cash received from option exercises 68.4      
Tax benefit realized from stock option exericses 19.9      
Excess tax benefit 13.9      
Restricted Stock        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Unrecognized compensation costs $ 0.4      
Unrecognized compensation costs, period for recognition, years 1 year 5 months      
Fair value of vested restricted stock $ 4.1 $ 4.3 $ 1.4  
Restricted Stock | Minimum        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting or deferral Period 1 year      
Restricted Stock | Maximum        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting or deferral Period 4 years