Goodwill and Intangible Assets (Schedule of Amortizable Intangible Assets) (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Jun. 30, 2024	Jun. 30, 2023	Jun. 30, 2024	Jun. 30, 2023	Sep. 30, 2023
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	$ 689.7		$ 689.7		$ 688.8
Amortizable intangible assets, accumulated amortization	331.8		331.8		307.9
Amortizable intangible assets, net	357.9		357.9		380.9
Other intangible assets, net	952.2		952.2		973.8
Intangible Assets, Gross (Excluding Goodwill)	1,284.0		1,284.0		1,281.7
Amortization of intangibles	7.7	$ 7.8	23.3	$ 23.2
Amortizable intangible assets, amortization expense, remainder of 2023	7.7		7.7
Amortizable intangible assets, amortization expense, fiscal 2024	31.1		31.1
Amortizable intangible assets, amortization expense, fiscal 2025	30.7		30.7
Amortizable intangible assets, amortization expense, fiscal 2026	30.5		30.5
Amortizable intangible assets, amortization expense, fiscal 2027	30.4		30.4
Amortizable intangible assets, amortization expense, fiscal 2028	30.3		30.3
Amortizable intangible assets, amortization expense, after fiscal 2028	197.2		197.2
Indefinite-lived intangible assets	594.3		594.3		592.9
Trade names and brands
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	339.7		339.7		339.6
Amortizable intangible assets, accumulated amortization	100.0		100.0		88.1
Amortizable intangible assets, net	239.7		239.7		251.5
Technology and patents
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	79.4		79.4		79.4
Amortizable intangible assets, accumulated amortization	76.8		76.8		76.2
Amortizable intangible assets, net	2.6		2.6		3.2
Customer related and other
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	270.6		270.6		269.8
Amortizable intangible assets, accumulated amortization	155.0		155.0		143.6
Amortizable intangible assets, net	$ 115.6		$ 115.6		$ 126.2