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Scientific Notation

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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

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

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

Move the decimal point 8 places to the left and use 8 as an exponent.

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.

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

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

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

ALGEBRA 1 LESSON 8-2

(continued)

3.8 1079.3 1074.84 1084.5 109

Mercury Earth JupiterNeptune

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 1056.03 104 610363.1 103

6.3 1026.03 1046.103 1036.31 104

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 1026.103 1036.03 1046.31 104

Write the original numbers in order.

0.0063 10561036.03 10463.1 103

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.

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

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