Income Taxes (Schedule of Components of Income before Income Taxes and the Consolidated Income Tax Provision) (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2019	Sep. 30, 2018	Sep. 30, 2017	Sep. 30, 2016
Income Tax Disclosures [Line Items]
Unrecognized Tax Benefits	$ 9.6	$ 6.2	$ 4.5	$ 5.1
Income before income taxes:
Domestic	122.5	101.8	129.0
Foreign	86.1	95.4	54.0
Total	208.6	197.2	183.0
Current provision
U.S. Federal	51.0	5.9	61.6
State	6.0	3.5	8.6
Foreign	18.2	20.2	13.3
Total current provision	75.2	29.6	83.5
Deferred provision:
U.S. Federal	(12.0)	(83.4)	(34.9)
State	(2.5)	(2.8)	1.3
Foreign	(4.3)	1.4	0.8
Total deferred provision	(18.8)	(84.8)	(32.8)
Income tax expense	$ 56.4	$ (55.2)	$ 50.7