Transcript Algebra - Selah High School

Scientific Notation
ALGEBRA 1 LESSON 8-2
Simplify each expression.
1. 6 • 104
2. 7 • 10–2
3. 8.2 • 105
4. 3 • 10–3
5. 3.4 • 101
6. 5.24 • 102
7. Simplify 3  102 + 6  101 + 7  100 + 8  10–1.
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Scientific Notation
ALGEBRA 1 LESSON 8-2
Solutions
1. 6 • 104 = 6 • 10,000 = 60,000
2. 7 • 10–2 = 7 • 0.01 = 0.07
3. 8.2 • 105 = 8.2 • 100,000 = 820,000
4.
5.
6.
7.
3 • 10–3 = 3 • 0.001 = 0.003
3.4 • 101 = 3.4 • 10 = 34
5.24 • 102 = 5.24 • 100 = 524
3  102 + 6  101 + 7  100 + 8  10–1
= (3  102) + (6  101) + (7  100) + (8  10–1)
= (3  100) + (6  10) + (7  1) + (8  0.1)
= 300 + 60 + 7 + 0.8
= 367.8
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Scientific Notation
ALGEBRA 1 LESSON 8-2
Is each number written in scientific notation? If not, explain.
a. 0.46  104
b. 3.25  10–2
c. 13.2  106
No;
0.46 is less than 1.
yes
No;
13.2 is greater than 10.
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Scientific Notation
ALGEBRA 1 LESSON 8-2
Write each number in scientific notation.
a. 234,000,000
234,000,000 = 2.34  108
Move the decimal point 8 places to the
left and use 8 as an exponent.
Drop the zeros after the 4.
b. 0.000063
0.000063 =
6.3  10–5
Move the decimal point 5 places to the
right and use –5 as an exponent.
Drop the zeros before the 6.
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Scientific Notation
ALGEBRA 1 LESSON 8-2
Write each number in standard notation.
a. elephant’s mass: 8.8  104 kg
8.8  104 = 8.8000.
A positive exponent indicates a
number greater than 10. Move the
decimal point 4 places to the right.
= 88,000
b. ant’s mass: 7.3  10–5 kg
7.3  10–5 = 0.00007.3
A negative exponent indicates a
number between 0 and 1. Move the
decimal point 5 places to the left.
= 0.000073
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Scientific Notation
ALGEBRA 1 LESSON 8-2
List the planets in order from least to greatest distance from
the sun.
Planet
Distance from
the Sun
Jupiter
4.84  108 mi
Earth
9.3  107 mi
Neptune
4.5  109 mi
Mercury
3.8  107 mi
Order the powers of 10. Arrange the decimals with the same power of 10
in order.
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Scientific Notation
ALGEBRA 1 LESSON 8-2
(continued)
3.8  107
Mercury
Planet
Distance from
the Sun
Jupiter
4.84  108 mi
Earth
9.3  107 mi
Neptune
4.5  109 mi
Mercury
3.8  107 mi
9.3  107
Earth
4.84  108
Jupiter
4.5  109
Neptune
From least to greatest distance from the sun, the order of the planets is
Mercury, Earth, Jupiter, and Neptune.
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Scientific Notation
ALGEBRA 1 LESSON 8-2
Order 0.0063  105, 6.03  104, 6103, and 63.1  103 from
least to greatest.
Write each number in scientific notation.
0.0063  105
6.3  102
6.03  104
63.1  103
6103
6.03  104
6.103  103
6.31  104
Order the powers of 10. Arrange the decimals with the same power of 10
in order.
6.3  102
6.103  103
6.03  104
6.31  104
Write the original numbers in order.
0.0063  105
6103
6.03  104
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63.1  103
Scientific Notation
ALGEBRA 1 LESSON 8-2
Simplify. Write each answer using scientific notation.
a. 6(8  10–4) = (6 • 8)  10–4
b.
Use the Associative Property of
Multiplication.
= 48  10–4
Simplify inside the parentheses.
= 4.8  10–3
Write the product in scientific notation.
0.3(1.3  103) = (0.3 • 1.3)  103
Use the Associative Property of
Multiplication.
= 0.39  103
Simplify inside the parentheses.
= 3.9  102
Write the product in scientific notation.
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Scientific Notation
ALGEBRA 1 LESSON 8-2
1. Write each number in scientific notation.
a. 0.00627
b. 3,486,000
6.27  10–3
3.486  106
2. Write each number in standard form.
a. 9.4  104
b. 2.3  10–6
94,000
0.0000023
3. Order the following numbers from least to greatest.
0.98  10–1, 1.6  103, 2.4  10–1, 11  100
0.98  10–1, 2.4  10–1, 11  100, 1.6  103
4. Simplify. Write the answer in scientific notation.
7(6.1  10–2) 4.27  10–1
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