Dominant chords are major chords with a flat 7th that sit on the 5th scale degree. There's a trick to easily finding them on the ukulele. First, start with the coolest chord ever, the diminished chord. You can play this anywhere on the ukulele fretboard.
What's cool about this chord, other than how mysterious and old timey it sounds, is that if you take any one note from it and you move it down one fret you end up with a dominant chord. Let's move the first note down.
If you've already learned a few chords, chances are you know these shapes already. If we shift any of these shapes down until one finger is off the fretboard, we end up with familiar chords. Does this first shape look familiar? Why, it's G7!
The little R under the 4th string indicates the location of the root of the chord. For all chords of this shape, the root will be on the 4th string. In addition to remembering these chord shapes, the roots are also important to remember. Roots are sometimes marked with a diamond instead of a circle.
If we move the second note of the diminished chord down one fret we get another major 7th chord. Let's move this shape down the fretboard to see if this is a familiar shape. Why it's good ol' C7 with a root on the 3rd string.
Moving the third note down gives us this chord, which is the E7 shape with a root on the 2nd string.
And finally, we have this chord, which is the A7 shape. The root for this shape is on the 1st string.
Isn't that neat? These are four common shapes for dominant chords. One easy way to remember where the roots are located: roots are on the same strings as the lowered notes from the diminished chord.
Chord diagrams generated by <uke-chord>