Page 25 - Theory and Problems of BEGINNING CHEMISTRY

14 MATHEMATICAL METHODS IN CHEMISTRY [CHAP. 2

EXAMPLE 2.5. (a) How many feet (ft) are there in 1.450 miles (mi)? (b) How many meters (m) are there in 1.450 kilometers
(km)?
5280 ft

Ans. (a)1.450 mi = 7656 ft
1mi
1000 m

(b)1.450 km = 1450 m
1km
You can do the calculation of part (b) in your head (merely move the decimal point in 1.450 three places to the right).
The calculation of part (a) requires a calculator or pencil and paper.

Instructors often require English-metric conversions for two purposes: to familiarize the student with the
relative sizes of the metric units in terms of the more familiar English units, and for practice in conversions
(Sec. 2.2). Once you really get into the course, the number of English-metric conversions that you do is very
small.
One of the main advantages of the metric system is that the same prefixes are used with all quantities, and
the prefixes always have the same meanings.

EXAMPLE 2.6. The unit of electric current is the ampere. What is the meaning of 1 milliampere?
Ans. 1 milliampere = 0.001 ampere 1 mA = 0.001 A
Even if you do not recognize the quantity, the prefix always has the same meaning.

EXAMPLE 2.7. How many centimeters are there in 5.000 m?
Ans. Each meter is 100 centimeters (cm); 5.000 m is 500.0 cm.

Area
The extent of a surface is called its area. The area of a rectangle (or a square, which is a rectangle with all
sides equal) is its length times its width.

A = l × w

The dimensions of area are thus the product of the dimensions of two distances. The area of a state or country
is usually reported in square miles or square kilometers, for example. If you buy interior paint, you can expect a
2
2
gallon of paint to cover about 400 ft . These units are stated aloud “square feet,” but are usually written ft . The
exponent (the superscript number) means that the unit is multiplied that number of times, just as it does with a
2
number. For example, ft means ft × ft.
2
EXAMPLE 2.8. State aloud the area of Rhode Island, 1214 mi .
Ans. “Twelve hundred fourteen square miles.”

EXAMPLE 2.9. A certain square is 3.0 m on each side. What is its area?
2
2
Ans. A = l = (3.0m) = 9.0m 2
Note the difference between “3 meters, squared” and “3 square meters.”
(3m) 2 and 3 m 2

The former means that the coefficient (3) is also squared; the latter does not.