Main Idea
NGSSS
Example 1: Multiplication and Division with
Scientific Notation
Example 2: Multiplication and Division with
Scientific Notation
Example 3: Real-World Example
Example 4: Addition and Subtraction with
Scientific Notation
Example 5: Addition and Subtraction with
Scientific Notation
Five-Minute Check
• Compute with numbers written in scientific
notation.
MA.8.A.6.1 Use exponents and scientific
notation to write large and small numbers
and vice versa and to solve problems.
MA.8.A.6.4 Perform operations on real
numbers (including integer exponents,
radicals, percents, scientific notation,
absolute value, rational numbers, and irrational
numbers) using multistep and real world
problems.
Multiplication and Division with
Scientific Notation
Evaluate (1.1 × 10–3)(2.5 × 109). Express the result
in scientific notation.
(1.1 × 10–3)(2.5 × 109)
= (1.1 × 2.5 )(10–3 × 109) Commutative and
Associative Properties
= (2.75)(10–3 × 109)
Multiply 1.1 by 2.5.
= 2.75 × 10–3 + 9
Product of Powers
= 2.75 × 106
Add the exponents.
Answer: 2.75 × 106
Evaluate (3.2 × 104)(1.9 × 10–8). Express the result
in scientific notation.
A. 6.08 × 104
B. 5.1 × 10–4
C. 6.08 × 10–4
D. 6.08 × 10–32
Multiplication and Division with
Scientific Notation
Evaluate
. Express the result in
scientific notation.
Associative Property
Divide 7.75 by 2.5.
= 3.1 × 106 – (–2)
Quotient of Powers
= 3.1 × 108
Subtract the exponents.
Answer: 3.1 × 108
Evaluate
scientific notation.
A. 3.5 × 10–10
B. 3.5 × 10–4
C. 3.5 × 104
D. 3.5 × 1010
. Express the result in
PLANETS The largest planet in our solar
system is Jupiter with a diameter of about
1.43 × 105 kilometers. The smallest planet in
our solar system is Mercury with a diameter of
about 4.9 × 103 kilometers. About how many
times greater is the diameter of Jupiter than
the diameter of Mercury?
Associative Property
≈ 0.29 × 102
Simplify.
≈ 2.9 × 101
Write 0.29 × 102 in
scientific notation.
Answer: The diameter of Jupiter is about 2.9 × 101
or 29 times greater than the diameter of
Mercury.
ASTRONOMY The mass of Jupiter is about
1.90 × 1027 kilometers. The mass of Pluto is about
1.29 × 1022 kilometers. About how many times
greater is the mass of Jupiter than the mass of
Pluto?
A. 1.47 × 101 times greater
B. 1.47 × 105 times greater
C. 6.1 × 104 times greater
D. 6.1 × 105 times greater
Addition and Subtraction with
Scientific Notation
Evaluate (2.85 × 107) + (1.61 × 109). Express the
result in scientific notation.
(2.85 × 107) + (1.61 × 109)
= (2.85 × 107) + (161 × 107) Write 1.61 × 109 as
161 × 107.
= (2.85 + 161) × 107
Distributive Property
= 163.85 × 107
Add 0.0285 and 1.61.
= 1.6385 × 109
Write 163.85 × 107 in
scientific notation.
Answer: 1.6385 × 109
Evaluate (3.78 × 105) + (5.12 × 106). Express the
result in scientific notation.
A. 8.9 × 1011
B. 5.498 × 105
C. 54.98 × 105
D. 5.498 × 106
Addition and Subtraction with
Scientific Notation
Evaluate (8.23 × 106) – (6.91 × 105). Express the
result in scientific notation.
(8.23 × 106) – (6.91 × 105)
= (82.3 × 105) – (6.91 × 105) Write 8.23 × 106 as
82.3 × 105.
= (82.3 – 6.91) × 105
Distributive Property
= 75.39 × 105
Subtract 6.91 from 82.3.
= 7.539 × 106
Write 75.39 × 105 in
scientific notation.
Answer: 7.539 × 106
Evaluate (7.54 × 105) – (1.22 × 103). Express the
result in scientific notation.
A. 6.32 × 102
B. 7.5278 × 104
C. 7.5278 × 105
D. 75.278 × 104
Evaluate (3.2 × 106)(2.8 × 102). Express the result
in scientific notation.
A. 8.96 × 108
B. 8.96 × 1012
C. 6.0 × 1012
D. 896 × 108
Evaluate
notation.
A. 2.75 × 102
B. 7.04 × 102
C. 7.04 × 1012
D. 2.75 × 1012
. Express the result in scientific
Evaluate (1.98 × 104) + (3.06 × 106). Express the
result in scientific notation.
A. 5.04 × 1010
B. 5.04 × 1024
C. 3.0798 × 106
D. 3.0798 × 104
Evaluate (2.99 × 1012) – (7.28 × 109). Express the
result in scientific notation.
A. –4.29 × 1012
B. –4.29 × 103
C. 2.9172 × 1012
D. 2.98272 × 1012
The empty weight of one airplane is
8.35 × 104 pounds, and the empty weight
of a second airplane is 3.07 × 105 pounds.
What is the difference in the empty
weights of these two airplanes?
A. 2.235 × 104 pounds
B. 2.235 × 105 pounds
C. 5.28 × 104 pounds
D. 5.28 × 105 pounds