Revenue (Disaggregation of Revenue by Geographical Region) (Details) $ in Millions	3 Months Ended
	Mar. 30, 2018 USD ($)
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	$ 4,695.4
North America
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	1,797.4
Western Europe
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	1,200.7
Other developed markets
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	312.6
High-growth markets
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	1,384.7
Life Sciences
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	1,476.0
Life Sciences | North America
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	480.4
Life Sciences | Western Europe
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	449.9
Life Sciences | Other developed markets
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	144.9
Life Sciences | High-growth markets
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	400.8
Diagnostics
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	1,519.7
Diagnostics | North America
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	607.4
Diagnostics | Western Europe
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	310.4
Diagnostics | Other developed markets
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	92.2
Diagnostics | High-growth markets
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	509.7
Dental
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	672.6
Dental | North America
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	291.3
Dental | Western Europe
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	175.6
Dental | Other developed markets
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	43.9
Dental | High-growth markets
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	161.8
Environmental & Applied Solutions
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	1,027.1
Environmental & Applied Solutions | North America
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	418.3
Environmental & Applied Solutions | Western Europe
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	264.8
Environmental & Applied Solutions | Other developed markets
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	31.6
Environmental & Applied Solutions | High-growth markets
Disaggregation of Revenue [Line Items]
Revenue from contract with customer, excluding assessed tax	$ 312.4