Instead of working with circle arcs, do it with complete circles with dashed strokes and change the dash and gap sizes.
In this example, starting with two circles blend (left), expanded and ungrouped it, add a dashed stroke and change the dash and gap size individually. Rotate the circles to match the position. Expand appearance when it's ready.
You can check the lengths of existing paths from Document info panel. There's subdialog Objects for it:
You can make circles with a wanted path length difference by drawing equally spaced full circles. The easy way is to draw 2 circles, align them to the same centerpoint, make a blend, expand the blend and ungroup it to get separate circles.
Then draw 2 ...
Perhaps I'm a gluten for punishment, but I'd do this simply with additional fills/strokes in the Appearance Panel... and the some transform Effects. This would tie the number to the circle.. and then I'd position them manually.
Select the text with the Selection Tool (Black Arrow)
Add a new Fill in the Appearance Panel
Highlight that new fill and...