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Income Taxes (Summary of Activity Related to Unrecognized Tax Benefits) (Details) - USD ($) $ in Millions | 12 Months Ended
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Oct. 03, 2021 | Sep. 27, 2020 | Sep. 29, 2019
Significant Change in Unrecognized Tax Benefits is Reasonably Possible [Line Items] |  |  |
Beginning balance | $ 123.7 | $ 132.1 | $ 224.6
Increase related to prior year tax positions | 4.8 | 11.1 | 3.8
Decrease related to prior year tax positions | (11.9) | (0.5) | (75.3)
Increase related to current year tax positions | 8.9 | 9.8 | 18.5
Decreases related to settlements with taxing authorities | (4.4) | 0.0 | (16.4)
Decreases related to lapsing of statute of limitations | (38.5) | (28.8) | (23.1)
Ending balance | 82.6 | 123.7 | 132.1
Gross unrecognized tax benefits | 82.6 | 123.7 | 132.1
Unrecognized tax benefits affecting the effective tax rate if recognized | 62.8 |  |
Interest and penalties expense/(benefit) recognized in income tax expense | 4.6 | (3.0) | $ 2.8
Accrued interest and penalties | $ 7.1 | $ 13.0 |

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