Share-Based Compensation (Narrative) (Details) - USD ($) $ / shares in Units, $ 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]
Shares available for future grant	1,500,000
Closing stock price (in dollars per share)	$ 232.73
Cash received from option exercises	$ 19.3	$ 10.6	$ 34.1
Total tax benefit realized from stock option exercises	11.2
Excess tax benefit from stock option exercises	$ 10.5
Deferred Stock Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of units/shares granted	195,000
Weighted-average grant date fair value (in dollars per share)	$ 329.65
Cash payments made for deferred stock units	$ 5.5	5.2	4.8
Unrecognized compensation costs	$ 56.0
Unrecognized compensation costs, period for recognition, years	1 year 7 months 6 days
Fair value of deferred stock units paid	$ 92.9	$ 88.0	$ 65.4
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	74,364	77,251	80,215
Weighted-average grant date fair value (in dollars per share)	$ 427.23	$ 235.48	$ 275.19
Time-Based Deferred Stock Unit
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of units/shares granted	120,996	110,555	123,448
Weighted-average grant date fair value (in dollars per share)	$ 278.67	$ 282.48	$ 230.92
Stock Options
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Weighted average remaining contractual terms, outstanding	1 year 3 months 18 days
Weighted average remaining contractual terms, exercisable	1 year 3 months 18 days
Aggregated intrinsic value, outstanding	$ 71.3
Aggregated intrinsic value, exercisable	71.3
Intrinsic value of stock options exercised	20.2	$ 29.0	$ 65.7
Cash received from option exercises	$ 19.3

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Aggregate cash paid by the entity during the period to settle equity instruments granted under equity-based payment arrangements.

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Amount of cost not yet recognized for nonvested award under share-based payment arrangement.

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Amount of cash inflow from exercise of option under share-based payment arrangement.

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The number of grants made during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan).

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Weighted average remaining contractual term for vested portions of options outstanding and currently exercisable or convertible, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

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