1. **Problem statement:** GN-z11 is 9.8 Giga parsecs (Gpc) away. We want to convert this distance to light years (ly) and kilometers (km). 2. **Given:** - 1 pc = 3.26 ly - 1 ly = 9.45 \times 10^{15} m - 1 Gpc = 10^9 pc - 1 km = 10^3 m 3. **Part (a): Convert Gpc to ly** - First convert 9.8 Gpc to parsecs: $$9.8 \text{ Gpc} = 9.8 \times 10^9 \text{ pc}$$ - Then convert parsecs to light years: $$9.8 \times 10^9 \text{ pc} \times 3.26 \frac{\text{ly}}{\text{pc}} = 9.8 \times 10^9 \times 3.26 \text{ ly}$$ - Calculate: $$9.8 \times 3.26 = 31.948$$ - So, $$9.8 \times 10^9 \text{ pc} = 3.1948 \times 10^{10} \text{ ly}$$ 4. **Part (b): Convert ly to km** - Convert light years to meters: $$3.1948 \times 10^{10} \text{ ly} \times 9.45 \times 10^{15} \frac{m}{ly} = 3.1948 \times 9.45 \times 10^{10 + 15} m$$ - Calculate the coefficient: $$3.1948 \times 9.45 = 30.19506$$ - So, $$30.19506 \times 10^{25} m = 3.019506 \times 10^{26} m$$ - Convert meters to kilometers: $$3.019506 \times 10^{26} m \times \frac{1 km}{10^3 m} = 3.019506 \times 10^{26 - 3} km = 3.019506 \times 10^{23} km$$ **Final answers:** - a) Distance in light years: $$3.1948 \times 10^{10} \text{ ly}$$ - b) Distance in kilometers: $$3.0195 \times 10^{23} \text{ km}$$