Income Taxes (Narrative) (Details) - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
	Sep. 30, 2019	Sep. 30, 2018	Sep. 30, 2017	Jun. 30, 2018	Sep. 30, 2016
Income Tax Disclosures [Line Items]
Deferred Tax Assets, Operating Loss Carryforwards, Foreign	$ 36.7
Global intangible low-taxed income- foreign tax deduction				50.00%
Deferred tax assets related to domestic federal net operating loss carryforwards	26.1
Deferred tax assets related to state net operating loss carryforwards	7.0
Deferred Tax Assets, State Tax Credits	22.6
Valuation Allowance, Deferred Tax Asset, Increase (Decrease), Amount	35.2
Valuation allowances on deferred tax assets	(45.0)	$ (80.2)
Impact of tax holidays	$ 5.2	$ 4.3	$ 3.6
Benefit of tax holidays on net income per share (diluted) (usd per share)	$ 0.08	$ 0.06	$ 0.05
Undistributed Earnings of Foreign Subsidiaries	$ 50.6
Total gross unrecognized tax benefits	9.6	$ 6.2	$ 4.5		$ 5.1
Unrecognized tax benefits that would impact effective tax rate, if recognized	9.3	5.6	3.3
Accrued interest and penalties related to unrecognized tax benefits	1.7	2.1	2.6
Income tax benefit for interest and penalties	$ 0.4	$ 0.5	0.4
Federal Corporate tax rate	21.00%	35.00%
Blended Corporate Tax rate	24.50%
Payment, Tax Withholding, Share-based Payment Arrangement	$ 4.7	$ 14.1	10.6
Deferred Tax Remeasurement, Amount	0.0	93.8	$ 0.0
Transition tax obligation, amount	1.0	$ 22.9
Tax Cuts and Jobs Act, Decrease in Deferred Tax Liability due to Transition Tax	1.0
Maximum [Member]
Income Tax Disclosures [Line Items]
Amount of reasonably possible decrease	7.3
UNITED STATES
Income Tax Disclosures [Line Items]
Total gross unrecognized tax benefits	$ 5.8