Income Taxes (Schedule of Differences between Income Tax Expense) (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2019	Sep. 30, 2018	Sep. 30, 2017
Income Tax Disclosure [Abstract]
Federal Corporate tax rate	21.00%	35.00%
Effective Income Tax Rate Reconciliation, Amount [Abstract]
Federal income tax	$ 43.8	$ 48.4	$ 64.1
State income tax	3.3	2.9	4.1
Foreign income tax	(10.1)	(25.9)	(35.6)
Application of federal research tax credits	(5.6)	(5.6)	(3.6)
Application of foreign tax credits	(0.1)	(1.0)	(15.0)
Valuation of tax attributes	2.2	23.4	36.3
Foreign inclusions	0.0	(0.9)	(11.5)
Domestic manufacturer’s deduction	0.0	(0.9)	(4.4)
Excess tax benefits from share based awards	5.2	16.1	8.9
Capitalized transaction costs	0.0	(9.2)	0.0
Other, net	1.0	(0.9)	3.0
Income tax expense	$ 56.4	$ (55.2)	$ 50.7
Effective Income Tax Rate Reconciliation, Percent [Abstract]
Federal income tax	21.00%	24.50%	35.00%
State income tax	1.60%	1.50%	2.20%
Foreign income tax	(4.90%)	(13.20%)	(19.40%)
Application of federal research tax credits	(2.70%)	(2.90%)	(2.00%)
Application of foreign tax credits	0.00%	(0.50%)	(8.20%)
Valuation of tax attributes	1.10%	11.90%	19.80%
Foreign inclusions	0.00%	(0.40%)	(6.30%)
Domestic manufacturer’s deduction	0.00%	(0.40%)	(2.40%)
Excess tax benefits from share based awards	2.50%	8.20%	4.90%
Capitalized transaction costs	0.00%	(4.70%)	0.00%
Other, net	0.40%	(0.40%)	1.70%
Income tax expense	27.00%	(28.00%)	27.70%
Deferred Tax Remeasurement, Amount	$ 0.0	$ (93.8)	$ 0.0
Deferred Tax Remeasurement, Percent	0.00%	(47.60%)	0.00%
Transition tax obligation, amount	$ (1.0)	$ (22.9)
Transition tax obligation, percent	(0.50%)	(11.60%)	0.00%
Foreign-derived Intangible Income Deduction	$ (4.3)	$ 0.0	$ 0.0
Foreign-derived Intangible Income Deduction, Percent	(2.00%)	0.00%	0.00%
GILTI inclusion	$ 9.6	$ 0.0	$ 0.0
GILTI Inclusion, Percent	4.60%	0.00%	0.00%
Effective Income Tax Rate Reconciliation, Disposition of Business, Amount	$ 18.2	$ 0.0	$ 0.0
Effective Income Tax Rate Reconciliation, Disposition of Business, Percent	8.70%	0.00%	0.00%
Current period change in uncertain tax positions	$ (4.6)	$ (1.5)	$ (0.8)
Current period change in uncertain tax positions, percent	2.20%	0.80%	0.40%