One gallon is equal to four quarts, so divide the number of quarts by 4 to convert to gallons. This means the tank has capacity $\displaystyle \frac{N}{4}$ gallons. Multiply this by $2.10, the price per gallon:

$\displaystyle \frac{N}{4} \cdot 2.10 = \frac{2.10 N}{4} = 0.525N$

This is the cost in dollars to fill the tank, so this is the correct choice.

There are 5280 feet in one mile.

Write the dimensional analysis and multiply by the given distance in miles.  We will want to have feet as the designated unit.

$\displaystyle 2.5 \textup{ miles }(\frac{5280 \textup{ feet}}{1 \textup{ mile}})= 13200 \textup{ feet}$

The answer is:  $\displaystyle 13200 \textup{ feet}$

For every centimeter, there is one-hundredth of a meter.

$\displaystyle 1 \textup{ cm} = \frac{1}{100} \textup{ m}$

To convert thirty centimeters to meters, simply multiply this number with the conversion factor.

$\displaystyle 30 \textup{ cm}\cdot \frac{1\textup{ m}}{100\textup{ cm}} = \frac{3}{10}\textup{ m}$

The answer is:  $\displaystyle \frac{3}{10}\textup{ m}$

There are 60 seconds in a minute.  Write the dimensional analysis.

$\displaystyle 1\textup{ minute }= 60\textup{ seconds}$

Multiply the given time by the dimensional analysis.

$\displaystyle 6\textup{ minutes }(\frac{60\textup{ seconds}}{1\textup{ minute }}) = 360\textup{ seconds}$

Notice that the minute units will cancel, leaving the answer in seconds.

The answer is:  $\displaystyle 360\textup{ seconds}$

There are 60 minutes in an hour.  Write the dimensional analysis.

$\displaystyle 60\textup{ minutes} = 1\textup{ hour}$

Multiply 25 minutes with the dimensional analysis as a fraction of the hours on the numerator and the minutes in the denominator.

$\displaystyle 25\textup{ minutes }(\frac{1\textup{ hour}}{60\textup{ minutes}})$

The minutes unit will cancel and leaves us with the hour unit.  Multiply and reduce the fraction.

$\displaystyle \frac{25}{60} = \frac{5 \times 5}{12 \times 5} = \frac{5}{12}$

The answer is:  $\displaystyle \frac{5}{12}\textup{ hour}$

There are 12 inches per foot.

Write the dimensional analysis.

$\displaystyle 12\textup{ inches }= 1\textup{ foot}$

Multiply the half inch with the dimensional analysis.  Make sure the foot unit is in the numerator and the inches unit is in the denominator so that they can be cancelled.

$\displaystyle \frac{1}{2}\textup{ inch }(\frac{1\textup{ foot}}{12\textup{ inches }}) = \frac{1}{24} \textup{ foot}$

The answer is:  $\displaystyle \frac{1}{24}$

There are $\displaystyle \textup{5280 feet}$ in a mile, and $\displaystyle \textup{3 feet}$ in a yard. Write both dimensional analyses.

$\displaystyle 5280\textup{ feet }= 1\textup{ mile}$

$\displaystyle 3\textup{ feet }= 1\textup{ yard}$

Multiply the $\displaystyle \textup{2 miles}$ by the conversion factors. Make sure that the mile and the feet units will cancel so that we will get the final unit in yards.

$\displaystyle 2\textup{ miles }\left (\frac{5280\textup{ feet }}{1\textup{ mile}} \right )\left (\frac{1\textup{ yard}}{3\textup{ feet }} \right ) = \frac{10560}{3} = 3520\textup{ yards}$

The answer is: $\displaystyle 3520\textup{ yards}$

There are $\displaystyle \textup{12 inches in a foot}$. Write the dimensional analysis.

$\displaystyle 1\textup{ foot }= 12\textup{ inches}$

Multiply the dimensional analysis with the given dimension. Be sure that the feet cancels in order to get the dimension in inches.

Multiply the fractions.

$\displaystyle \frac{4}{7}\textup{ feet } \left (\frac{12\textup{ inches}}{1\textup{ foot}} \right ) = \frac{48}{7}\textup{ inches}$

The answer is: $\displaystyle \frac{48}{7}$

There are 1000 meters in a kilometer.

Write the equation to express this dimensional analysis.

$\displaystyle 1\textup{ kilometer }= 1000\textup{ meters}$

Multiply the dimension with conversion factor.  Make sure that the meters unit will cancel.

$\displaystyle 2.35\textup{ meters }(\frac{1\textup{ kilometer}}{1000\textup{ meters}})$

Dividing by 1000 is similar to moving the decimal place back three places.

The answer is:  $\displaystyle 0.00235 \textup{ kilometer}$