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Segment Disclosures - Segment Earnings from Operations (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 03, 2021	Dec. 29, 2019	Dec. 30, 2018
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Gross profit	$ 827.6	$ 968.4	$ 972.2
SG&A expenses	(805.6)	(883.1)	(884.8)
Earnings (loss) from operations	(93.6)	81.8	87.4
Gain (loss) on investment in Persol Holdings	(16.6)	35.8	(96.2)
Other income (expense), net	3.4	(1.2)	(0.6)
Earnings (loss) before taxes and equity in net earnings (loss) of affiliate	(106.8)	116.4	(9.4)
Corporate
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Earnings (loss) from operations	(203.8)	(97.6)	(94.1)
Professional & Industrial | Reporting Segments
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Gross profit	330.2	388.4	419.3
SG&A expenses	(288.6)	(326.0)	(338.4)
Earnings (loss) from operations	41.6	62.4	80.9
Science, Engineering & Technology | Reporting Segments
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Gross profit	209.4	226.2	185.6
SG&A expenses	(134.4)	(146.7)	(124.7)
Earnings (loss) from operations	75.0	79.5	60.9
Education | Reporting Segments
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Gross profit	42.2	72.0	70.7
SG&A expenses	(51.2)	(56.2)	(47.8)
Earnings (loss) from operations	(9.0)	15.8	22.9
Outsourcing & Consulting | Reporting Segments
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Gross profit	119.8	122.3	124.2
SG&A expenses	(108.3)	(119.3)	(131.2)
Earnings (loss) from operations	11.5	3.0	(7.0)
International | Reporting Segments
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Gross profit	126.0	159.5	172.4
SG&A expenses	(134.9)	(140.8)	(148.6)
Earnings (loss) from operations	$ (8.9)	$ 18.7	$ 23.8

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This item represents the net total realized and unrealized gain (loss) included in earnings for the period as a result of selling or holding marketable securities categorized as trading, available-for-sale, or held-to-maturity, including the unrealized holding gain (loss) of held-to-maturity securities transferred to the trading security category and the cumulative unrealized gain (loss) which was included in other comprehensive income (a separate component of shareholders' equity) for available-for-sale securities transferred to trading securities during the period. Additionally, this item would include any gains (losses) realized during the period from the sale of investments accounted for under the cost method of accounting.

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