Chemistry Reference
In-Depth Information
Some of these steps could have been combined for a more efficient solution
process.
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 can often help 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 7.5 yd
(Figure 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 mul-
tiplied 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 (Figure A.1b):
yard
2
yard
yard
Be careful to distinguish between similarly worded phrases, such as “3.00 yards,
squared” and “3.00 square yards” (Figure A.2).
EXAMPLE A.6
What is the unit of the volume of a cubic box whose edge measures 2.0 ft?
Solution
A cube has the same length along each of its edges, so the volume is
(2.0 ft)
3
8.0 ft
3
V
The unit is
ft
3
ft
ft
ft
Practice Problem A.6
What is the unit of the price of (a) eggs?
(b) milk?
15.0 yd
Figure 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.
(Not drawn to scale.)
(a)
7.5 yd
7.5 yd
1 yd
2
1 yd
(b)
1 yd
