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Share-Based Compensation (Narrative) (Details)
$ / shares in Units, $ in Millions
12 Months Ended
Oct. 03, 2016
$ / shares
Sep. 30, 2019
USD ($)
$ / shares
shares
Sep. 30, 2018
USD ($)
$ / shares
shares
Sep. 30, 2017
USD ($)
$ / shares
shares
Sep. 30, 2016
$ / shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Shares available for future grant | shares   4,581,960      
Closing stock price (in dollars per share) | $ / shares $ 140.38 $ 221.86     $ 150.35
Cash received from option exercises   $ 68.1 $ 76.2 $ 68.4  
Conversion ratio for separation adjustments 1.071        
Deferred Stock Units          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Number of units/shares granted | shares   285,000      
Weighted-average grant date fair value (in dollars per share) | $ / shares   $ 193.29      
Cash payments made for deferred stock units   $ 1.9 2.2 2.1  
Unrecognized compensation costs   $ 49.2      
Unrecognized compensation costs, period for recognition, years   1 year 7 months      
Fair value of deferred stock units paid   $ 19.2 $ 38.5 $ 36.6  
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   114,929 105,268 117,692  
Weighted-average grant date fair value (in dollars per share) | $ / shares   $ 229.61 $ 202.50 $ 156.87  
Time-Based Deferred Stock Unit          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Number of units/shares granted | shares   169,666 143,379 165,121  
Weighted-average grant date fair value (in dollars per share) | $ / shares   $ 168.68 $ 162.11 $ 143.75  
Stock Options          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Vesting or deferral period   3 years      
Unrecognized compensation costs   $ 0.0      
Exercisable period from grant date   10 years      
Intrinsic value of stock options exercised   $ 87.2 $ 90.4 $ 57.3  
Cash received from option exercises   68.1      
Tax benefit realized from stock option exericses   20.4      
Excess tax benefit   16.4      
Restricted Stock          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Unrecognized compensation costs   0.0      
Fair value of vested restricted stock   $ 2.6 $ 2.2 $ 4.1  
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