Round your answer to 3 significant digits. 1.47 light-years to miles (a light-year is an astronomical measure of the distance traveled by light in a year, or 365 days; the speed of light is \( 2.998 \times 10^{8} \frac{\mathrm{~m}}{\mathrm{~s}} ; 1 \mathrm{~km}=0.6125 \mathrm{mi} \) )

To convert 1.47 light-years to miles, we follow these steps: 1. **Calculate the Distance Light Travels in One Year:** - **Speed of Light (\( c \))**: \( 2.998 \times 10^{8} \, \text{m/s} \) - **Seconds in a Year**: \( 365 \, \text{days} \times 24 \, \text{hours/day} \times 60 \, \text{minutes/hour} \times 60 \, \text{seconds/minute} = 31,536,000 \, \text{seconds} \) - **Distance in One Year**: \( c \times \text{seconds in a year} = 2.998 \times 10^{8} \, \text{m/s} \times 31,536,000 \, \text{s} = 9.454 \times 10^{16} \, \text{meters} \) 2. **Convert Meters to Miles:** - **Meters to Kilometers**: \( 9.454 \times 10^{16} \, \text{meters} \div 1,000 = 9.454 \times 10^{13} \, \text{kilometers} \) - **Kilometers to Miles**: \( 9.454 \times 10^{13} \, \text{km} \times 0.6125 = 5.781 \times 10^{13} \, \text{miles} \) 3. **Adjust for 1.47 Light-Years:** - **Total Miles**: \( 5.781 \times 10^{13} \, \text{miles/year} \times 1.47 \, \text{years} = 8.51 \times 10^{12} \, \text{miles} \) **Final Answer:** \[ 1.47 \, \text{light-years} \approx 8.51 \times 10^{12} \, \text{miles} \]