I'm using Mudder.js to do it, but the algorithm is straightforward. Define an alphabet (e.g., A-Z). Every time an item is inserted/repositioned, its sort order is given the midpoint between the sort values of its two neighbors. So the first item is given the sort value M (midpoint between A and Z). Inserting before that item gets G (between A and M). Inserting between these two items gets J (between G and M).

Once you run out of letters between two sort values, the algorithm tacks a digit onto the sort value of the item ahead of it. So inserting between M and N yields MM. If you do this enough times in a pathological pattern and wind up with some long string of characters you can reflow your list and rebalance everything out evenly (though that's strictly an optimization for storage space/bandwidth, and not a requirement for the algorithm to function).

This all sorts perfectly with ORDER BY etc., supports an number of repositions bounded only by your storage space, and doesn't require arbitrary-precision decimal datatypes or fraction handling.