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Stock-Based Compensation - Schedule of Outstanding Stock Options (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
Sep. 30, 2020
Sep. 30, 2019
Sep. 30, 2018
Sep. 30, 2017
Share-based Compensation Arrangement by Share-based Payment Award        
Stock Option Awards Outstanding, Number Outstanding (in shares) 1,083,402 1,328,390 1,268,984 1,531,691
Stock Option Awards Outstanding, Weighted-Average Remaining Contractual Life, (in years) 6 years 8 months 12 days      
Weighted-Average Exercise Price of Outstanding Options (in dollars per share) $ 74.38 $ 62.62 $ 57.03 $ 45.14
Stock Option Awards Outstanding, Aggregate Intrinsic Value $ 6.5      
Stock Option Awards Exercisable, Number Exercisable (in shares) 537,241 709,826 650,143  
Stock Option Awards Exercisable, Weighted-Average Remaining Contractual Life (in years) 4 years 10 months 24 days      
Options exercisable, end of year (in dollars per share) $ 68.16 $ 55.11 $ 45.92  
Stock Option Awards Exercisable, Aggregate Intrinsic Value $ 4.9      
Price Range, $40.00 - $60.00        
Share-based Compensation Arrangement by Share-based Payment Award        
Stock Option Awards Outstanding, Exercise Prices, Low End of Range (in dollars per share) $ 40.00      
Stock Option Awards Outstanding, Exercise Prices, High End of Range (in dollars per share) $ 60.00      
Stock Option Awards Outstanding, Number Outstanding (in shares) 99,514      
Stock Option Awards Outstanding, Weighted-Average Remaining Contractual Life, (in years) 1 year 8 months 12 days      
Weighted-Average Exercise Price of Outstanding Options (in dollars per share) $ 43.26      
Stock Option Awards Outstanding, Aggregate Intrinsic Value $ 3.0      
Stock Option Awards Exercisable, Number Exercisable (in shares) 99,514      
Stock Option Awards Exercisable, Weighted-Average Remaining Contractual Life (in years) 1 year 8 months 12 days      
Options exercisable, end of year (in dollars per share) $ 43.26      
Stock Option Awards Exercisable, Aggregate Intrinsic Value $ 3.0      
Price Range, $60.01 - $80.00        
Share-based Compensation Arrangement by Share-based Payment Award        
Stock Option Awards Outstanding, Exercise Prices, Low End of Range (in dollars per share) $ 60.01      
Stock Option Awards Outstanding, Exercise Prices, High End of Range (in dollars per share) $ 80.00      
Stock Option Awards Outstanding, Number Outstanding (in shares) 493,958      
Stock Option Awards Outstanding, Weighted-Average Remaining Contractual Life, (in years) 6 years 2 months 12 days      
Weighted-Average Exercise Price of Outstanding Options (in dollars per share) $ 66.41      
Stock Option Awards Outstanding, Aggregate Intrinsic Value $ 3.5      
Stock Option Awards Exercisable, Number Exercisable (in shares) 282,819      
Stock Option Awards Exercisable, Weighted-Average Remaining Contractual Life (in years) 4 years 8 months 12 days      
Options exercisable, end of year (in dollars per share) $ 66.64      
Stock Option Awards Exercisable, Aggregate Intrinsic Value $ 1.9      
Price Range, $80.01 - $100.00        
Share-based Compensation Arrangement by Share-based Payment Award        
Stock Option Awards Outstanding, Exercise Prices, Low End of Range (in dollars per share) $ 80.01      
Stock Option Awards Outstanding, Exercise Prices, High End of Range (in dollars per share) $ 100.00      
Stock Option Awards Outstanding, Number Outstanding (in shares) 489,930      
Stock Option Awards Outstanding, Weighted-Average Remaining Contractual Life, (in years) 8 years 3 months 18 days      
Weighted-Average Exercise Price of Outstanding Options (in dollars per share) $ 88.73      
Stock Option Awards Exercisable, Number Exercisable (in shares) 154,908      
Stock Option Awards Exercisable, Weighted-Average Remaining Contractual Life (in years) 7 years 3 months 18 days      
Options exercisable, end of year (in dollars per share) $ 86.93