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12 Chemistry: Matter and Change
Solving Problems: A Chemistry Handbook
SOLVING PROBLEMS:
A CHEMISTRY HANDBOOK
CHAPTER
2
Adding and subtracting using scientific notation To add or
subtract quantities written in scientific notation, the quantities must
have the same exponent. For example, 4.5 ϫ 10 14 m ϩ 2.1 ϫ 10 14 m
ϭ 6.6 ϫ 10 14 m. If two quantities are expressed to different powers
of ten, you must change one of the quantities so that they are both
expressed to the same power of ten before you add or subtract them.
Example Problem 2-5
Adding Quantities Written in Scientific Notation
Solve the following problem.
2.45 ϫ 10 14 kg ϩ 4.00 ϫ 10 12 kg
First express both quantities to the same power of ten. Either quantity
can be changed. For example, you might change 2.45 ϫ 10 14 to 245
ϫ 10 12 . Then add the quantities: 245 ϫ 10 12 kg ϩ 4.00 ϫ 10 12 kg
ϭ 249 ϫ 10 12 kg. Write the final answer in scientific notation: 2.49
ϫ 10 14 kg.
Practice Problems
14. Solve the following addition and subtraction problems. Write
your answers in scientific notation.
a. 5.10 ϫ 10 20 ϩ 4.11 ϫ 10 21
b. 6.20 ϫ 10 8 Ϫ 3.0 ϫ 10 6
c. 2.303 ϫ 10 5 Ϫ 2.30 ϫ 10 3
d. 1.20 ϫ 10 Ϫ4 ϩ 4.7 ϫ 10 Ϫ5
e. 6.20 ϫ 10 Ϫ6 ϩ 5.30 ϫ 10 Ϫ5
f. 8.200 ϫ 10 2 Ϫ 2.0 ϫ 10 Ϫ1
Multiplying and dividing using scientific notation When
multiplying or dividing quantities written in scientific notation, the
quantities do not have to have the same exponent. For multiplication,
multiply the first factors, then add the exponents. For division,
divide the first factors, then subtract the exponents.
Example Problem 2-6
Multiplying Quantities Written in Scientific Notation
Solve the following problem.
(2 ϫ 10 14 cm) ϫ (4 ϫ 10 12 cm)
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