Nudge shapes (move their position by a small amount) by using the keyboard arrow keys. Press an arrow key once to apply a single nudge increment, or hold down an arrow key to nudge repeatedly.
The nudge distance (distance moved per key press) is always a whole fraction of the grid spacing, or in other words there are always a whole number of nudges per grid space.
The number of nudges per grid space is determined by the current zoom setting. At higher zoom percentages each grid space is sub-divided into more nudge increments, to allow for finer work.
The nudge distance per key press can be modified with these keyboard shortcuts: ⇧ Shift: move 10x, ⌥⇧ Option-Shift: move 0.2x.
The following table shows the number of nudges per grid space for different zoom ranges:
NOTE: You can change the grid spacings via the Document Inspector.