Worked example - find a star's absolute magnitude. A star has a measured parallax of 0.05 arcseconds and an apparent magnitude m = 8.0. Step 1: distance d = 1/p = 1/0.05 = 20 parsecs. Step 2: distance modulus m - M = 5 log(d/10) = 5 log(2) = 5 x 0.301 = 1.505. Step 3: M = m - 1.505 = 8.0 - 1.505 = 6.5. So from the standard 10-parsec distance it would shine at magnitude 6.5 - just at the naked-eye limit, and intrinsically fainter than the Sun (M_sun = +4.83).