1. **State the problem:** Gayle wants to buy a bicycle costing 119.90. She has saved 0.7 of the total cost. We need to find how much she has saved so far. 2. **Formula used:** To find the amount saved, multiply the total cost by the fraction saved: $$\text{Amount saved} = \text{Total cost} \times \text{Fraction saved}$$ 3. **Substitute values:** $$\text{Amount saved} = 119.90 \times 0.7$$ 4. **Calculate:** $$\text{Amount saved} = 83.93$$ 5. **Interpretation:** Gayle has saved 83.93 so far towards buying the bicycle. **Final answer:** $$\boxed{83.93}$$