  Recent observations of the nearby Galactic molecular clouds indicate that the
dense gas in molecular clouds have quasi-universal properties on star
formation, and observational studies of extra galaxies have shown a
galactic-scale correlation between the star formation rate (SFR) and surface
density of molecular gas. To reach a comprehensive understanding of both
properties, it is important to quantify the fractional mass of the dense gas in
molecular clouds f_DG. In particular, for the Milky Way (MW), there are no
previous studies resolving the f_DG disk over a scale of several kpc. In this
study, the f_DG was measured over 5kpc in the first quadrant of the MW, based
on the CO J=1-0 data in l=10-50 deg obtained as part of the FOREST Unbiased
Galactic Plane Imaging Survey with the Nobeyama 45-m Telescope (FUGIN) project.
The total molecular mass was measured using 12CO, and the dense gas mass was
estimated using C18O. The fractional masses including f_DG in the region within
~30% of the distances to the tangential points of the Galactic rotation (e.g.,
the Galactic Bar, Far-3kpc Arm, Norma Arm, Scutum Arm, Sagittarius Arm, and
inter-arm regions) were measured. As a result, an averaged f_DG of
2.9^{+2.6}_{-2.6} % was obtained for the entirety of the target region. This
low value suggests that dense gas formation is the primary factor of
inefficient star formation in galaxies. It was also found that the f_DG shows
large variations depending on the structures in the MW disk. The f_DG in the
Galactic arms were estimated to be ~4-5%, while those in the bar and inter-arm
regions were as small as ~0.1-0.4%. These results indicate that the
formation/destruction processes of the dense gas and their timescales are
different for different regions in the MW, leading to the differences in SFRs.
