1. **Problem:** To increase the current price $P$ of an item by 9.9%, find the multiplier to apply to $P$. 2. **Formula:** To increase a quantity by a percentage $r\%$, multiply by $1 + \frac{r}{100}$. 3. **Calculation:** Here, $r = 9.9$, so the multiplier is: $$1 + \frac{9.9}{100} = 1 + 0.099 = 1.099$$ 4. **Explanation:** Multiplying $P$ by 1.099 adds 9.9% of $P$ to itself, increasing the price by 9.9%. **Final answer:** $1.099$