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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. 02, 2022 | Oct. 03, 2021 | Sep. 27, 2020
Significant Change in Unrecognized Tax Benefits is Reasonably Possible [Line Items] |  |  |
Beginning balance | $ 82.6 | $ 123.7 | $ 132.1
Increase related to prior year tax positions | 0.2 | 4.8 | 11.1
Decrease related to prior year tax positions | (0.7) | (11.9) | (0.5)
Increase related to current year tax positions | 9.0 | 8.9 | 9.8
Decreases related to settlements with taxing authorities | 0.0 | (4.4) | 0.0
Decreases related to lapsing of statute of limitations | (1.4) | (38.5) | (28.8)
Ending balance | 89.7 | 82.6 | 123.7
Gross unrecognized tax benefits | 89.7 | 82.6 | 123.7
Unrecognized tax benefits affecting the effective tax rate if recognized | 65.1 |  |
Interest and penalties expense/(benefit) recognized in income tax expense | 2.3 | (4.6) | $ (3.0)
Accrued interest and penalties | $ 9.4 | $ 7.1 |

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