A star's parallax is measured in arc seconds, where 1 arc second = 0.00027 of a degree!! This is the angle subtended by a dime at a distance of 2 kilometers! The nearest star to use is Proxima Centauri, which has a parallax of about 0.75 arc seconds. This is why astronomers can only measure the distance of close stars (using parallax), only as far as 300 light years -- which is less than 1 percent the diameter of our galaxy, the Milky Way.
