Average number of automobile drivers, \(n = 210 \times {10^6}\)

Average distance covered by each car, \({d_{{\rm{av}}}} = 15000\;{\rm{mi}}/{\rm{yr}}\)

Average fuel efficiency, \(mpg = 23.6\;{\rm{mil}}/{\rm{gal}}\)

A gallon is a measuring unit of liquid capacity.One US gallon is equal to 3.785 liters or 128 fluid ounces.

The total distance covered by all automobiles is the product of the average number of drivers and the distance covered by each automobile in a year.

The total number of miles covered by all automobiles in a year is \(D = n \times {d_{{\rm{av}}}}\).

Substituting the variables by the known values in the above equation, you get

\(\begin{aligned}{c}D = 210 \times {10^6} \times 15000\;{\rm{mi}}/{\rm{yr}}\\ = 31.5 \times {10^{11}}\;{\rm{mi}}/{\rm{yr}}{\rm{.}}\end{aligned}\)

The order-of-magnitude estimate of any physical quantity is rounded to the nearest power of 10.

It is given that each car has \(23.6\;{\rm{mil}}/{\rm{gal}}\) of gasoline.

The total number of gallons of gasoline consumed by all automobiles per year is \(Q = \frac{D}{{mpg}}\).

Substituting the variables by the known values in the above equation, you get

\(\begin{aligned}{c}Q = \frac{{31.5 \times {{10}^{11}}\;{\rm{mi}}/{\rm{yr}}}}{{23.6\;{\rm{mil}}/{\rm{gal}}}}\\ = 1.3 \times {10^{11}}\;{\rm{gal}}/{\rm{yr}}{\rm{.}}\end{aligned}\)

Thus, the order-of-magnitude estimate of the gasoline consumed per year is \({10^{11}}\;{\rm{gal}}/{\rm{yr}}\).