Dividing the number of cultured cells per volume (2.8e11 cells / 3 mL), you have 9.33e10 cells per mL. Performing the same calculation for what you need to give the mice (1.0e9 cells / 0.1 mL) yields 1.00e10 cells per mL. Dividing the concentrations of what you have (9.33e10 cells per mL) by what you need (1.00e10 cells per mL), the concentration of your cells is about 9.33-fold more concentrated than what you need to give the mice.
Unless you are limited to specifically making 100 microL (which can be prone to error when diluting cells), you can take any amount of your cultured cells and dilute them about 9.33-fold to get what you need. I would simply take 1 mL of your cultured cells and dilute them to a final volume of 9.33 mL, then take 100 microL from this to give to the mice.
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