How to label each section of a polar grid with type on a path tool?

Using the Rotate tool should work if you are working carefully. It is a very precise tool.

However, you may take the following .ai file (ca. 100 kb) to get another possible way.

https://drive.google.com/file/d/1Hp2Njrgl7Yy-KjnpcDJBbriB2hzL-7Jb/view?usp=sharing

Instruction:

- Download, unzip and open the file.
- Save a copy of the file, so you can examine it later.
- In the Layers palette, there is a main layer called "H_2".
- Select the entire layer "H_2".
- In the Brushes palette, there is a scatter brush called "Placeholder_2".
- Apply this brush to the current selection.
- Go to the Object menu and choose the Expand Appearance command.
- Ungroup, if desired.

Now you can change each placeholder digit to something different.

You can also select all type objects (point type), convert them to area type objects in the Type menu and then make threaded text, as Ton did in his example.

Depending on the actual numbers you are going to use, one would have to modify the procedure a bit, but I think the basic idea may be clear.

I did not use type on a path tool but rotated threaded text boxes.

It is best to create a new layer for the text.

There are different ways to do it, but you may just prepare one type object with a "dummy" number and the desired dimensions and at a precise position, then take the Rotate tool, set its reference point to the centre of the entire construction and copy rotate, followed by hitting Cmd/Ctrl-D (Transform Again command) to repeat as often as necessary.

After that, you can change the content of the dummies to the numbers you want.

As already mentioned, there are other ways that may even be a bit easier or at least quicker.

Which version of Illustrator are you using?

Also, can you show a sketch that may explain how you want to arrange the numbers?