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Solving Problems: A Chemistry Handbook
Chemistry: Matter and Change
13
SOLVING PROBLEMS:
A CHEMISTRY HANDBOOK
CHAPTER
2
To solve the multiplication problem, first multiply the factors:
2 ϫ 4 ϭ 8. Then add the exponents: 14 ϩ 12 ϭ 26. Combine the
factors: 8 ϫ 10 26 . Finally, multiply the units and write your answer
in scientific notation: 8 ϫ 10 26 cm 2 .
Practice Problems
15. Solve the following multiplication and division problems. Write
your answers in scientific notation.
a. (12 ϫ 10 4 m) ϫ (5 ϫ 10 Ϫ2 m)
b. (3 ϫ 10 7 km) ϫ (3 ϫ 10 7 km)
c. (2 ϫ 10 Ϫ4 mm) ϫ (2 ϫ 10 Ϫ4 mm)
d. (90 ϫ 10 14 kg) Ϭ (9 ϫ 10 12 L)
e. (12 ϫ 10 Ϫ4 m) Ϭ (3 ϫ 10 Ϫ4 s)
f. (20 ϫ 10 15 km) Ϭ (5 ϫ 10 11 s)
Dimensional analysis Dimensional analysis is a method of
problem solving that focuses on the units that are used to describe
matter. Dimensional analysis often uses conversion factors. A
conversion factor is a ratio of equivalent values used to express the
same quantity in different units. A conversion factor is always equal
to 1. Multiplying a quantity by a conversion factor does not change
its value—because it is the same as multiplying by 1—but the units
of the quantity can change.
Example Problem 2-7
Converting From One Unit to Another Unit
How many centigrams are in 5 kilograms?
Two conversion factors are needed to solve this problem. Remember
that there are 1000 grams in a kilogram and 100 centigrams in a
gram. To determine the number of centigrams in 1 kilogram, set up
the first conversion factor so that kilograms cancel out. Set up the
second conversion factor so that grams cancel out.
5 kg ϫ
ϫ
ϭ500,000 cg
100 cg
ᎏ
1 g
1000 g
ᎏ
1 kg
▲
Solving Problems: A Chemistry Handbook
Chemistry: Matter and Change
13
SOLVING PROBLEMS:
A CHEMISTRY HANDBOOK
CHAPTER
2
To solve the multiplication problem, first multiply the factors:
2 ϫ 4 ϭ 8. Then add the exponents: 14 ϩ 12 ϭ 26. Combine the
factors: 8 ϫ 10 26 . Finally, multiply the units and write your answer
in scientific notation: 8 ϫ 10 26 cm 2 .
Practice Problems
15. Solve the following multiplication and division problems. Write
your answers in scientific notation.
a. (12 ϫ 10 4 m) ϫ (5 ϫ 10 Ϫ2 m)
b. (3 ϫ 10 7 km) ϫ (3 ϫ 10 7 km)
c. (2 ϫ 10 Ϫ4 mm) ϫ (2 ϫ 10 Ϫ4 mm)
d. (90 ϫ 10 14 kg) Ϭ (9 ϫ 10 12 L)
e. (12 ϫ 10 Ϫ4 m) Ϭ (3 ϫ 10 Ϫ4 s)
f. (20 ϫ 10 15 km) Ϭ (5 ϫ 10 11 s)
Dimensional analysis Dimensional analysis is a method of
problem solving that focuses on the units that are used to describe
matter. Dimensional analysis often uses conversion factors. A
conversion factor is a ratio of equivalent values used to express the
same quantity in different units. A conversion factor is always equal
to 1. Multiplying a quantity by a conversion factor does not change
its value—because it is the same as multiplying by 1—but the units
of the quantity can change.
Example Problem 2-7
Converting From One Unit to Another Unit
How many centigrams are in 5 kilograms?
Two conversion factors are needed to solve this problem. Remember
that there are 1000 grams in a kilogram and 100 centigrams in a
gram. To determine the number of centigrams in 1 kilogram, set up
the first conversion factor so that kilograms cancel out. Set up the
second conversion factor so that grams cancel out.
5 kg ϫ
ϫ
ϭ500,000 cg
100 cg
ᎏ
1 g
1000 g
ᎏ
1 kg
▲