For your cleaning solution, it is not possible to calculate the pH of the solution after dilution. Above all, the so-called sodium metasilicate is not a pure compound - it is a mixture of several low-molecular silicates (see wikipedia - sodium metasilicate). The pH calculation can only be performed if you know the exact composition of the solution. Also, due to the composition of the solution, pH measurement is problematic. However, you can try to estimate the pH change of the solution after 200 fold dilution. For a pure NaOH solution, the pH will drop by 2.3 pH units.
For a clean Na2SiO3 solution, the pH of the diluted solution will drop by approximately 1.2 pH units. If after dilution of the solution your solution is clear, you may expect a pH about 10.3 or slightly higher. If the solution is opalescent, the pH will be slightly less than 10.3.