  Accurate multiplicities of prompt fission neutrons emitted in neutron-induced
fission on a large energy range are essential for fundamental and applied
nuclear physics. Measuring them to high precision for radioactive fissioning
nuclides remains, however, an experimental challenge. In this work, the average
prompt-neutron multiplicity emitted in the 239Pu(n,f) reaction was extracted as
a function of the incident-neutron energy, over the range 1-700~MeV, with a
novel technique, which allowed to minimize and correct for the main sources of
bias and thus achieve unprecedented precision.
  At low energies, our data validate for the first time the ENDF/B-VIII.0
nuclear data evaluation with an independent measurement and reduce the
evaluated uncertainty by up to $60\%$. This work opens up the possibility of
precisely measuring prompt fission neutron multiplicities on highly radioactive
nuclei relevant for an essential component of energy production world-wide.
