Question E.8: Unit Conversions Involving Units Raised to a Power Calculate...
Unit Conversions Involving Units Raised to a Power
Calculate the displacement (the total volume of the cylinders through which the pistons move) of a 5.70-L automobile engine in cubic inches.
SORT Sort the information in the problem into given and find.
GIVEN: 5.70 L
FIND: in³
STRATEGIZE Write a conceptual plan. Begin with the given information and devise a path to the information that you are asked to find. Notice that for cubic units, you must cube the
conversion factors.
CONCEPTUAL PLAN
RELATIONSHIPS USED
1 \ mL = 10^{-3} \ L
1 mL = 1 cm³
2.54 cm = 1 in
(These conversion factors are in the inside back cover of your book.)
SOLVE Follow the conceptual plan to solve the problem. Round the answer to three significant figures to reflect the three significant figures in the least precisely known quantity (5.70 L). These conversion factors are all exact and therefore do not limit the number of significant figures.
5.70 \ \cancel{L}\times\frac{1 \ \cancel{mL}}{10^{-3} \ \cancel{L}} \times \frac{1 \ \cancel{cm^3}}{1 \ \cancel{mL}} \times \frac{(1 \ in)^3}{(2.54 \ \cancel{cm})^3} =347.835 \ in^3 = 348 \ in^3CHECK The units of the answer are correct, and the magnitude makes sense. The unit cubic inches is smaller than liters, so the volume in cubic inches should be larger than the volume in liters.