We measure the hadronic branching ratios of the Z0 boson into heavy quarks: Rb=ΓZ0→bb¯/ΓZ0→hadrons and Rc=ΓZ0→cc¯/ΓZ0→hadrons using a multitag technique. The measurement was performed using about 400 000 hadronic Z0 events recorded in the SLC Large Detector experiment at SLAC between 1996 and 1998. The small and stable SLAC Linear Collider beam spot and the CCD-based vertex detector were used to reconstruct bottom and charm hadron decay vertices with high efficiency and purity, which enables us to measure most efficiencies from data. We obtain, Rb=0.21604±0.00098(stat.)±0.00073(syst.)∓0.00012(Rc) and, Rc=0.1744±0.0031(stat.)±0.0020(syst.)∓0.0006(Rb).1 MoreReceived 18 May 2005DOI:https://doi.org/10.1103/PhysRevD.71.112004©2005 American Physical Society