Shareholders' Equity (Narrative) (Details) - USD ($) $ / shares in Units, $ in Millions	3 Months Ended	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Equity [Abstract]
Common shares, authorized (in shares)	300,000,000	300,000,000	300,000,000.0
Shares available for future awards (in shares)	4,600,000	4,600,000
Preferred shares, par value (in usd per share)	$ 0.01	$ 0.01	$ 0.01
Preferred shares, outstanding (in shares)			0
Shares withheld for taxes on equity based compensation (in shares)		200,000
Treasury Stock, Shares, Acquired		1,900,000
Treasury Stock, Value, Acquired, Cost Method		$ 75.2	$ 125.3	$ 9.2
Shares available for repurchase under authorization		4.6
Common Stock, Dividends, Per Share, Declared	$ 0.15
Preferred shares, authorized (in shares)	10,000,000.0	10,000,000.0	10,000,000
Dividends declared to common shareholders		$ 31.7	$ 32.6	33.7
Dividends paid		$ 31.5	$ 32.6	$ 25.6