Share-Based Compensation (Narrative) (Details) - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares available for future grant	1,566,433
Closing stock price (in dollars per share)	$ 256.11
Cash received from option exercises	$ 10.6	$ 34.1	$ 68.1
Total tax benefit realized from stock option exercises	6.8
Excess tax benefit from stock option exercises	$ 6.5
Deferred Stock Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of units/shares granted	188,000
Weighted-average grant date fair value (in dollars per share)	$ 261.95
Cash payments made for deferred stock units	$ 5.2	4.8	1.9
Unrecognized compensation costs	$ 47.0
Unrecognized compensation costs, period for recognition, years	1 year 6 months
Fair value of deferred stock units paid	$ 88.0	$ 65.4	$ 19.2
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	77,251	80,215	114,929
Weighted-average grant date fair value (in dollars per share)	$ 235.48	$ 275.19	$ 229.61
Time-Based Deferred Stock Unit
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of units/shares granted	110,555	123,448	169,666
Weighted-average grant date fair value (in dollars per share)	$ 282.48	$ 230.92	$ 168.68
Stock Options
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting or deferral period	3 years
Exercisable period from grant date	10 years
Weighted average remaining contractual terms, outstanding	1 year 10 months 24 days
Weighted average remaining contractual terms, exercisable	1 year 10 months 24 days
Aggregated intrinsic value, outstanding	$ 125.0
Aggregated intrinsic value, exercisable	125.0
Intrinsic value of stock options exercised	29.0	$ 65.7	$ 87.2
Cash received from option exercises	$ 10.6

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