Goodwill and Intangible Assets (Schedule of Amortizable Intangible Assets) (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	$ 692.0	$ 688.8
Amortizable intangible assets, accumulated amortization	(341.2)	(307.9)
Amortizable intangible assets, net	350.8	380.9
Amortization of intangibles	31.1	30.8	$ 29.4
Amortizable intangible assets, amortization expense, next 12 months	31.1
Amortizable intangible assets, amortization expense, year two	30.8
Amortizable intangible assets, amortization expense, year 3	30.5
Amortizable intangible assets, amortization expense, year 4	30.5
Amortizable intangible assets, amortization expense, year 5	30.4
Amortizable intangible assets, amortization expense, thereafter	197.5
Indefinite-lived intangible assets	597.7	592.9
Intangible Assets, Gross (Excluding Goodwill)	1,289.7	1,281.7
Other intangible assets, net	948.5	973.8
Trade names and brands
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	339.8	339.6
Amortizable intangible assets, accumulated amortization	(104.0)	(88.1)
Amortizable intangible assets, net	235.8	251.5
Technology and patents
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	79.7	79.4
Amortizable intangible assets, accumulated amortization	(77.3)	(76.2)
Amortizable intangible assets, net	2.4	3.2
Customer related and other
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	272.5	269.8
Amortizable intangible assets, accumulated amortization	(159.9)	(143.6)
Amortizable intangible assets, net	$ 112.6	$ 126.2