Parts per million can be a bit hard to calculate (you would have to take the mass of your liquids, and know the normal ppm of the dishwashing liquid you're using), but I think percentage would work fine! Just be sure to report whether you are doing percentage by mass or by volume.
It would probably be easiest to measure the percentage by volume:
You will need glassware that can measure in mililiters. Keeping in mind that there are 1,000 mL in 1L, you can calculate that you would need 100 mL of DW liquid (.1*1000) and 900 mL of water to make a 10% DW liquid solution by volume. Double check to make sure that combining the two liquids makes a 1L solution, and you're all set! You can use this math to create all the other solutions. Please reply below if you need further help with the calculations
To calculate % by mass:
This way is a little more work, but if the liquids don't combine to make 1 liter exactly, you might want to try this.
If you have a scale, some measuring glassware, and a calculator handy, you can calculate your percentage by mass. Getting an exact liter this way would take a lot of guess and check, so I'd recommend you do this: Measure out amounts of water and DW liquid that correspond to your percentages and combine to make over a liter (ex: 40 grams of DW liquid + 360 grams of water = a 400 g, 10% DW liquid solution by mass... 40 g DW/400g total = 10%. Just make sure it makes more than a liter total in volume!) Mix the liquids together thoroughly, and pour out 1L of your mixed solution. Voila! A 10% DW liquid solution by mass.
Good luck, and please let me know if you are confused by anything or have more questions!