Income Taxes (Schedule of Differences between Income Tax Expense) (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019
Effective Income Tax Rate Reconciliation, Amount [Abstract]
Federal income tax	$ 63.6	$ 57.0	$ 43.8
State income tax	7.3	4.1	3.3
Foreign income tax	(17.9)	(15.0)	(10.1)
Application of federal research tax credits	(7.7)	(6.2)	(5.6)
Application of foreign tax credits	(9.5)	(11.6)	(0.1)
Valuation of tax attributes	1.2	5.0	2.2
Foreign inclusions	(10.3)	(7.7)	0.0
Excess tax benefits from share based awards	1.5	4.7	5.2
Other, net	4.0	3.0	1.0
Income tax expense	$ 54.3	$ 48.2	$ 56.4
Effective Income Tax Rate Reconciliation, Percent [Abstract]
Federal income tax	21.00%	21.00%	21.00%
State income tax	2.40%	1.50%	1.60%
Foreign income tax	(5.90%)	(5.50%)	(4.90%)
Application of federal research tax credits	(2.60%)	(2.30%)	(2.70%)
Application of foreign tax credits	3.20%	4.30%	0.00%
Valuation of tax attributes	0.40%	1.90%	1.10%
Foreign inclusions	(3.50%)	(2.90%)	0.00%
Excess tax benefits from share based awards	0.50%	1.70%	2.50%
Other, net	1.30%	1.10%	0.40%
Income tax expense	17.90%	17800000.00%	27000000.00%
Transition tax obligation, amount	$ 0.0	$ 0.0	$ 1.0
Transition tax obligation, percent	0.00%	0.00%	0.50%
Foreign-derived Intangible Income Deduction	$ (9.9)	$ (7.8)	$ (4.3)
Foreign-derived Intangible Income Deduction, Percent	(3.40%)	2.90%	2.00%
GILTI inclusion	$ 7.6	$ 12.6	$ 9.6
GILTI Inclusion, Percent	2.60%	4.60%	4.60%
Effective Income Tax Rate Reconciliation, Disposition of Business, Amount	$ 0.0	$ 4.1	$ 18.2
Effective Income Tax Rate Reconciliation, Disposition of Business, Percent	0.00%	(1.50%)	8.70%
Current period change in uncertain tax positions	$ 0.0	$ 0.0	$ 4.6
Current period change in uncertain tax positions, percent	0.00%	0.00%	(2.20%)
Effective Income Tax Rate Reconciliation, Nondeductible Expense, Percent	2.30%
Effective Income Tax Rate Reconciliation, Nondeductible Expense, Amount	$ 6.8