Washing soda has been for many years the common name listed in the CRC Handbook for Sodium Carbonate decahydrate, which has 10 molecules of water of crystallization in each molecule. We usually use either the monohydrate or the anhydrous salt. Washing soda SHOULD be cheap. It used to be very commonly available and used for cleaning auto radiators and general cleaning. Now it returns with a flourish that makes it seem quite special. The chances are that pH Plus or other brand of swimming pool "medicine" will be more suitable, although I did use in days gone by washing soda in developing printing paper. I had a stabilazion processor that used special paper that could be developed in a strong alkali and fixed in standard fixer. A handful of washing soda in a gallon or so of water made a very fine developer for that stuff. The paper was double weight fiber based and good for exhibition prints, but that's another story.
If you need a more precisely measurable carbonate and all you have is washing soda, you can heat a pan of it in the oven at about 200 F. Weigh it before you start and stop heating when it stops losing weight. You can do the same with baking soda. It will not burn and the gas emitted at that temperature is water vapor. If you are sure it really is washing soda, you can allow for the water in it by using 2.7 times as much.