Goodwill and Intangible Assets (Schedule of Amortizable Intangible Assets) (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	$ 688.8	$ 684.3
Amortizable intangible assets, accumulated amortization	307.9	274.7
Amortizable intangible assets, net	380.9	409.5
Amortization of intangibles	30.8	29.4	$ 22.0
Amortizable intangible assets, amortization expense, next 12 months	31.0
Amortizable intangible assets, amortization expense, year two	31.0
Amortizable intangible assets, amortization expense, year 3	30.6
Amortizable intangible assets, amortization expense, year 4	30.4
Amortizable intangible assets, amortization expense, year 5	30.3
Amortizable intangible assets, amortization expense, thereafter	227.6
Indefinite-lived intangible assets	592.9	587.1
Intangible Assets, Gross (Excluding Goodwill)	1,281.7	1,271.4
Other intangible assets, net	973.8	996.6
Trade names and brands
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	339.6	339.4
Amortizable intangible assets, accumulated amortization	88.1	72.2
Amortizable intangible assets, net	251.5	267.2
Technology and patents
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	79.4	77.8
Amortizable intangible assets, accumulated amortization	76.2	75.0
Amortizable intangible assets, net	3.2	2.8
Customer related and other
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	269.8	267.1
Amortizable intangible assets, accumulated amortization	143.6	127.5
Amortizable intangible assets, net	$ 126.2	$ 139.6