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