Page 306 - Theory and Problems of BEGINNING CHEMISTRY

APP.] SCIENTIFIC CALCULATIONS 295

EXAMPLE A.5. What is the unit of the volume of a cubic box whose edge measures 2.00 ft?
Ans. A cube has the same length along each of its edges, so the volume is
3
V = (2.00 ft) = 8.00 ft 3
The unit is: ft × ft × ft = ft 3
The unit of a quantity may be treated as an algebraic variable. For example, how many liters of soda are
purchased if someone buys a 1.00-L bottle of soda plus three 2.00-L bottles of soda?
1.00 L + 3(2.00 L) = 7.00 L
The same result would have been obtained if L were an algebraic variable instead of a unit. In dollars, how much
will the 7.00 L of soda cost if the average price is 89 cents per liter?
89 cents 1 dollar

7.00 L = 623 cents = 6.23 dollars
1L 100 cents
EXAMPLE A.6. What is the unit of the price of ground meat at the supermarket?

Ans. The price is given in dollars per pound.

If two or more quantities representing the same type of measurement—for example, a distance—are multi-
plied, they are usually expressed in the same unit. For example, to calculate the area of a rug that is 9.0 ft wide
and 4.0 yd long, we express the length and the width in the same unit before they are multiplied. The width in
yards is
1yd

9.0ft = 3.0yd
3ft
The area is
(4.0yd)(3.0yd) = 12 yd 2
If we had multiplied the original measurements without first converting one to the unit of the other, we would
have obtained an incomprehensible set of units:
(9.0ft)(4.0yd) = 36 ft·yd

EXAMPLE A.7. What is the cost of 8.00 ounces (oz) of hamburger if the store charges $2.98 per pound?
Ans. Do not simply multiply:
2.98 dollars 23.84 oz·dollar

8.00 oz =
1lb lb
Instead, first convert one of the quantities to a unit that matches that of the other quantity:
1lb

8.00 oz = 0.500 lb
16 oz
2.98 dollars

0.500 lb = 1.49 dollars
1lb
The same principles apply to the metric units used in science.
EXAMPLE A.8. A car accelerates from 10.0 mi/h to 40.0 mi/h in 10.0 s. What is the acceleration of the car? (Acceleration
is the change in velocity per unit of time.)
Ans. The change in velocity is
40.0 mi/h − 10.0 mi/h = 30.0 mi/h
30.0 mi/h 3.00 mi/h
=
10.0s s