1. **State the problem:** We need to find the ratio of gold to silver to bronze medals won by Switzerland in the 2010 Winter Olympic Games. 2. **Identify the values:** From the table, Switzerland won 6 gold, 0 silver, and 3 bronze medals. 3. **Write the ratio:** The ratio is $6:0:3$. 4. **Simplify the ratio:** Since the silver medals are zero, the ratio remains $6:0:3$. 5. **Divide each term by the greatest common divisor (GCD):** The GCD of 6 and 3 is 3. $$\frac{6}{\cancel{3}} : \frac{0}{\cancel{3}} : \frac{3}{\cancel{3}} = 2 : 0 : 1$$ 6. **Final answer:** The simplest form of the ratio of gold to silver to bronze medals for Switzerland is $2:0:1$. This means for every 2 gold medals, Switzerland won 0 silver and 1 bronze medal.