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Reporting Segment And Geographic Information (Schedule Of Revenue, Operating Income And Identifiable Assets By Segment) (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Jan. 03, 2020	Sep. 27, 2019	Jun. 28, 2019	Mar. 29, 2019	Dec. 28, 2018	Sep. 28, 2018	Jun. 29, 2018	Mar. 30, 2018	Jan. 03, 2020	Dec. 28, 2018	Dec. 29, 2017
Segment Reporting Information [Line Items]
Revenue	$ 824.0	$ 783.9	$ 854.8	$ 801.6	$ 785.5	$ 795.2	$ 785.5	$ 742.2	$ 3,264.3	$ 3,108.4	$ 2,646.5
Acquired deferred revenue adjustment									7.0	23.6	2.8
Operating Income (Loss)									375.9	320.7	235.7
Amortization of Deferred Sales Commissions									(6.3)	(4.7)	(1.3)
Depreciation									39.4	35.6	34.6
Building and Infrastructure [Member]
Segment Reporting Information [Line Items]
Revenue									1,254.2	1,065.5	829.4
Acquired deferred revenue adjustment									4.0	22.2	1.1
Amortization of Deferred Sales Commissions									(6.2)	(4.5)	(0.9)
Geospatial [Member]
Segment Reporting Information [Line Items]
Revenue									649.4	723.1	658.5
Acquired deferred revenue adjustment									0.0	0.0	0.0
Resources and Utilities [Member]
Segment Reporting Information [Line Items]
Revenue									568.4	567.1	481.0
Acquired deferred revenue adjustment									3.0	1.0	1.0
Amortization of Deferred Sales Commissions									(0.1)	(0.2)	(0.1)
Transportation [Member]
Segment Reporting Information [Line Items]
Revenue									792.3	752.7	677.6
Acquired deferred revenue adjustment									0.0	0.4	0.7
Amortization of Deferred Sales Commissions										0.0	(0.3)
Operating Segments [Member]
Segment Reporting Information [Line Items]
Revenue									3,271.3	3,132.0	2,649.3
Operating Income (Loss)									747.1	734.6	558.3
Depreciation									23.2	21.1	20.0
Operating Segments [Member] \| Building and Infrastructure [Member]
Segment Reporting Information [Line Items]
Revenue									1,258.2	1,087.7	830.5
Operating Income (Loss)									319.9	256.7	176.2
Depreciation									8.1	6.4	6.2
Operating Segments [Member] \| Geospatial [Member]
Segment Reporting Information [Line Items]
Revenue									649.4	723.1	658.5
Operating Income (Loss)									132.2	166.4	129.4
Depreciation									6.3	6.0	5.4
Operating Segments [Member] \| Resources and Utilities [Member]
Segment Reporting Information [Line Items]
Revenue									571.4	568.1	482.0
Operating Income (Loss)									169.1	168.2	137.9
Depreciation									4.4	4.2	3.2
Operating Segments [Member] \| Transportation [Member]
Segment Reporting Information [Line Items]
Revenue									792.3	753.1	678.3
Operating Income (Loss)									125.9	143.3	114.8
Depreciation									4.4	4.5	5.2
Segment Reconciling Items [Member]
Segment Reporting Information [Line Items]
Operating Income (Loss)									746.4	715.7	556.8
Segment Reconciling Items [Member] \| Building and Infrastructure [Member]
Segment Reporting Information [Line Items]
Operating Income (Loss)									322.1	239.0	176.0
Segment Reconciling Items [Member] \| Geospatial [Member]
Segment Reporting Information [Line Items]
Operating Income (Loss)									132.2	166.4	129.4
Segment Reconciling Items [Member] \| Resources and Utilities [Member]
Segment Reporting Information [Line Items]
Operating Income (Loss)									166.2	167.4	137.0
Segment Reconciling Items [Member] \| Transportation [Member]
Segment Reporting Information [Line Items]
Operating Income (Loss)									$ 125.9	$ 142.9	$ 114.4