Which is more likely the distance from Earth to the sun, \( 1.5 \times 10^{9} \mathrm{ml} \) \( 1.5 \times 10^{-8} \mathrm{mi} \) ?

To determine which distance is more likely the distance from Earth to the Sun, we can convert both distances into a common unit and compare them. 1. **Convert \( 1.5 \times 10^{9} \mathrm{ml} \) to miles:** - There are \( 1,609,344 \) milliliters in a gallon and \( 1 \) gallon is approximately \( 0.008 \) miles. However, since we are dealing with milliliters, we need to convert milliliters to liters first: - \( 1 \mathrm{ml} = 0.001 \mathrm{l} \) - Therefore, \( 1.5 \times 10^{9} \mathrm{ml} = 1.5 \times 10^{6} \mathrm{l} \). - Now, converting liters to gallons: - \( 1 \mathrm{l} \approx 0.264172 \mathrm{gallons} \) - So, \( 1.5 \times 10^{6} \mathrm{l} \approx 1.5 \times 10^{6} \times 0.264172 \approx 396,258 \mathrm{gallons} \). - Finally, converting gallons to miles: - \( 1 \mathrm{gallon} \approx 0.008 \mathrm{miles} \) - Therefore, \( 396,258 \mathrm{gallons} \approx 396,258 \times 0.008 \approx 3,169 \mathrm{miles} \). 2. **Convert \( 1.5 \times 10^{-8} \mathrm{mi} \) to miles:** - This is already in miles, so \( 1.5 \times 10^{-8} \mathrm{mi} \) is simply \( 0.000000015 \mathrm{mi} \). 3. **Comparison:** - The distance from Earth to the Sun is approximately \( 93,000,000 \mathrm{mi} \) or \( 1.5 \times 10^{8} \mathrm{mi} \). - Comparing the two distances: - \( 1.5 \times 10^{9} \mathrm{ml} \approx 3,169 \mathrm{miles} \) - \( 1.5 \times 10^{-8} \mathrm{mi} \approx 0.000000015 \mathrm{miles} \) Clearly, \( 1.5 \times 10^{9} \mathrm{ml} \) (approximately \( 3,169 \mathrm{miles} \)) is much closer to the actual distance from Earth to the Sun than \( 1.5 \times 10^{-8} \mathrm{mi} \). Thus, the more likely distance from Earth to the Sun is \( 1.5 \times 10^{9} \mathrm{ml} \).