1. **State the problem:** We know that 19.9% of all registered doctors were female, and the number of female doctors is 41,300. We need to find the total number of registered doctors. 2. **Formula used:** To find the total amount when given a percentage of a partial amount, use the formula: $$\text{Total} = \frac{\text{Partial amount}}{\text{Percentage as a decimal}}$$ 3. **Convert the percentage to a decimal:** $$19.9\% = \frac{19.9}{100} = 0.199$$ 4. **Apply the formula:** $$\text{Total} = \frac{41,300}{0.199}$$ 5. **Simplify the division:** $$\text{Total} = 207,537.6884...$$ 6. **Round to the nearest whole number:** $$\boxed{207,538}$$ So, the total number of registered doctors is approximately 207,538.