Scientific Notation

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Scientific Notation. ALGEBRA 1 LESSON 8-2. (For help, go to Lesson 8-1.). Simplify each expression. 1. 6 • 10 4 2. 7 • 10 –2 3. 8.2 • 10 5 4. 3 • 10 –3 5. 3.4 • 10 1 6. 5.24 • 10 2 7. Simplify 3  10 2 + 6  10 1 + 7  10 0 + 8  10 –1. 8-2. Scientific Notation.

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Scientific Notation

ALGEBRA 1 LESSON 8-2

(For help, go to Lesson 8-1.)

Simplify each expression.

1. 6 • 1042. 7 • 10–23. 8.2 • 105

4. 3 • 10–35. 3.4 • 1016. 5.24 • 102

7. Simplify 3  102 + 6  101 + 7  100 + 8  10–1.

8-2

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. 3 • 10–3 = 3 • 0.001 = 0.003

5. 3.4 • 101 = 3.4 • 10 = 34

6. 5.24 • 102 = 5.24 • 100 = 524

7. 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

8-2

Scientific Notation

ALGEBRA 1 LESSON 8-2

Is each number written in scientific notation? If not, explain.

a. 0.46  104

No; 0.46 is less than 1.

b. 3.25  10–2

yes

c. 13.2  106

No; 13.2 is greater than 10.

8-2

2.34  108

234,000,000 =

Drop the zeros after the 4.

Move the decimal point 5 places to the right and use –5 as an exponent.

6.3  10–5

0.000063 =

Drop the zeros before the 6.

Scientific Notation

ALGEBRA 1 LESSON 8-2

Write each number in scientific notation.

a. 234,000,000

b. 0.000063

8-2

A positive exponent indicates a number greater than 10. Move the decimal point 4 places to the right.

8.8  104 =

8.8000.

A negative exponent indicates a number between 0 and 1. Move the decimal point 5 places to the left.

7.3  10–5 =

0.00007.3

Scientific Notation

ALGEBRA 1 LESSON 8-2

Write each number in standard notation.

a. elephant’s mass: 8.8  104 kg

= 88,000

b. ant’s mass: 7.3  10–5 kg

= 0.000073

8-2

Distance from

the Sun

Planet

4.84  108 mi

Jupiter

9.3  107 mi

Earth

4.5  109 mi

Neptune

3.8  107 mi

Mercury

Scientific Notation

ALGEBRA 1 LESSON 8-2

List the planets in order from least to greatest distance from the sun.

Order the powers of 10. Arrange the decimals with the same power of 10 in order.

8-2

Distance from

the Sun

Planet

4.84  108 mi

Jupiter

9.3  107 mi

Earth

4.5  109 mi

Neptune

3.8  107 mi

Mercury

Scientific Notation

ALGEBRA 1 LESSON 8-2

(continued)

3.8  107 9.3  107 4.84  108 4.5  109

Mercury Earth Jupiter Neptune

From least to greatest distance from the sun, the order of the planets isMercury, Earth, Jupiter, and Neptune.

8-2

Write each number in scientific notation.

0.0063 105 6.03  104 6103 63.1  103

6.3  102 6.03  104 6.103  103 6.31  104

Scientific Notation

ALGEBRA 1 LESSON 8-2

Order 0.0063  105, 6.03  104, 6103, and 63.1  103 from least to greatest.

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 63.1  103

8-2

Use the Associative Property of Multiplication.

(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

=

= 0.39 103

Simplify inside the parentheses.

= 3.9  102

Write the product in scientific notation.

Scientific Notation

ALGEBRA 1 LESSON 8-2

Simplify. Write each answer using scientific notation.

6(8 10–4)

a.

0.3(1.3 103)

b.

8-2

Scientific Notation

ALGEBRA 1 LESSON 8-2

1. Write each number in scientific notation.

a.  0.00627

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

0.0000023

0.98  10–1, 2.4  10–1, 11  100, 1.6  103

4.27  10–1

8-2