Page 305 - Theory and Problems of BEGINNING CHEMISTRY

294 SCIENTIFIC CALCULATIONS [APP.

Ans. Inverting each side of the equation yields
F − 32.0 9
=
t 5
9
Simplifying gives F = t + 32.0
5
EXAMPLE A.4. Using the equation in Example A.3, find the value of F if t = 25.0.
9
9
Ans. F = t + 32.0 = (25.0) + 32.0 = 77.0
5 5
UNITS
Perhaps the biggest difference between ordinary algebra and scientific algebra is that scientific measurements
(and most other measurements) are always expressed with units. Like variables, units have standard symbols.
The units are part of the measurements and very often help you determine what operation to perform.
Units are often multiplied or divided, but never added or subtracted. (The associated quantities may be added
or subtracted, but the units are not.) For example, if we add the lengths of two ropes, each of which measures
4.00 yards (Fig. A-1a), the final answer includes just the unit yards (abbreviated yd). Two units of distance are
multiplied to get area, and three units of distance are multiplied to get the volume of a rectangular solid (such as
a box). For example, to get the area of a carpet, we multiply its length in yards by its width in yards. The result
has the unit square yards (Fig. A-1 b):
Yard × yard = yard 2

8.00 yd
4 yd 16 yd 2

4.00 yd 4.00 yd 4 yd
(a) (b)
Fig. A-1. Addition and multiplication of lengths
(a) When two (or more) lengths are added, the result is a length, and the unit is a unit of length, such as yard.
(b) When two lengths are multiplied, the result is an area, and the unit is the square of the unit of length, such as
square yards.

Be careful to distinguish between similarly worded phrases, such as 2.00 yards, squared and 2.00 square
yards (Fig. A-2).

1 yd 2 1 yd 2
2 yd
2 square yards

2 yd
2 yards, squared
Fig. A-2. An important difference in wording
Knowing the difference between such phrases as 2 yards, squared and 2 square yards is important. Multiplying
2 yards by 2 yards gives 2 yards, squared, which is equivalent to 4 square yards, or four blocks with sides 1 yard
long, as you can see. In contrast, 2 square yards is two blocks, each having sides measuring 1 yard.