Answer :
Final answer:
The correct conversion factor for converting cubic miles to cubic feet is 1 = 147,197,952,000 cubic feet / 1 cubic mile. This allows us to multiply a cubic mile figure by the factor to get the result in cubic feet, ensuring the units cancel correctly. So, the correct option is option D.
Explanation:
To find a conversion factor between cubic feet and cubic miles, we start with the given equivalence that 147,197,952,000 cubic feet equals 1 cubic mile. To convert cubic miles to cubic feet, we need a conversion factor that will cancel out cubic miles and leave us with cubic feet. The correct form for this conversion factor, therefore, is: 1 = 147,197,952,000 cubic feet / 1 cubic mile. To find a conversion factor between cubic feet and cubic miles, we can use the given information: 147197952000 cubic feet = 1 cubic mile. We want to convert from cubic miles to cubic feet, so we need to write the conversion factor in that form. The correct option is D.
Therefore, the conversion factor is 1 = 147,197,952,000 cubic feet / 1 cubic mile. We write the factor in this form so that when we multiply any number of cubic miles by this factor, the unit cubic miles will cancel out, leaving the result in cubic feet. This approach to unit conversion is based on the idea that a conversion factor is a ratio that equals one and does not change the value of the measurement, only the units. For example: If we want to convert 2 cubic miles to cubic feet, we multiply 2 by the conversion factor: 2 cubic miles * 147,197,952,000 cubic feet / 1 cubic mile = 294,395,904,000 cubic feetThe cubic mile units cancel out, and the answer is in cubic feet.
