1) The document provides examples of writing numbers in standard form and scientific notation. It also gives examples of performing arithmetic operations such as addition, subtraction, multiplication, and division on numbers expressed in scientific notation. 2) The examples illustrate how writing very large or very small numbers in scientific notation makes it easier to perform operations with them. It also allows for estimating quantities that would otherwise be difficult to comprehend in standard form. 3) Understanding scientific notation helps to compare quantities that differ vastly in magnitude, such as populations and diameters of astronomical objects. It enables estimating ratios and relative sizes in a straightforward manner.

1. Course 3, Lesson 1-7
Write each number in standard form.
1. 5.92 × 104 2. 1.9 × 10–6 3. 6.7 × 108
Write each number in scientific notation.
4. 26,400,000 5. 11,000 6. 0.000098
7. The diameter of Jupiter at its equator is approximately
143,000 kilometers. Write this number in scientific
notation.

2. Course 3, Lesson 1-7
ANSWERS
1. 59,200
2. 0.0000019
3. 670,000,000
4. 2.64 × 107
5. 1.1 × 104
6. 9.8 × 10–5
7. 1.43 × 105

3. WHY is it helpful to write numbers in
different ways?
The Number System
Course 3, Lesson 1-7

4. Course 3, Lesson 1-7 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of
Chief State School Officers. All rights reserved.
The Number System
• 8.EE.3
Use numbers expressed in the form of a single digit times an integer
power of 10 to estimate very large or very small quantities, and to
express how many times as much one is than the other.
• 8.EE.4
Perform operations with numbers expressed in scientific notation,
including problems where both decimal and scientific notation are used.
Use scientific notation and choose units of appropriate size for
measurements of very large or very small quantities. Interpret scientific
notation that has been generated by technology.

5. Course 3, Lesson 1-7 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of
Chief State School Officers. All rights reserved.
The Number System
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.

6. To
• add, subtract, multiply and divide
with numbers written in scientific
notation
Course 3, Lesson 1-7
The Number System

7. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
1. Evaluate (7.2 × 103)(1.6 × 104). Express the
result in scientific notation.
(7.2 × 103)(1.6 × 104) = (7.2 × 1.6)(103 × 104)
= (11.52)(103 × 104)
= 11.52 × 103 + 4
= 11.52 × 107
= 1.152 × 108
Commutative and
Associative Properties
Multiply 7.2 by 1.6.
Product of Powers
Add the exponents.
Write in scientific notation.

8. Answer
Need Another Example?
Evaluate (1.1 × 10–3)(2.5 × 109). Express the
result in scientific notation.
2.75 × 106

9. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
2. In 2010, the world population was about 6,860,000,000. The population
of the United States was about 3 × 108. About how many times larger is
the world population than the population of the United States?
Estimate the population of the world and write in scientific notation.
6,860,000,000 ≈ 7,000,000,000 or 7 × 109
Find .
=
≈ 2.3 ×
Associative Property
Divide 7 by 3. Round to the nearest tenth.
Quotient of Powers
7
≈ 2.3 × 101
So, the population of the world is about 23 times larger
than the population of the United States.
≈ 2.3 × 109 – 8
Subtract the exponents.

10. Answer
Need Another Example?
The largest planet in our solar system is Jupiter
with a diameter of about 143,000 kilometers.
The smallest planet in our solar system is
Mercury with a diameter of about 5 × 103
kilometers. About how many times greater is the
diameter of Jupiter than the diameter of
Mercury?
Sample answer: 3 × 101 or 30 times greater

11. 1
Need Another Example?
2
3
4
Step-by-Step Example
3. Evaluate the expression. Express the result in
scientific notation.
(6.89 × 104) + (9.24 × 105)
(6.89 × 104) + (9.24 × 105)
= (6.89 + 92.4) × 104
Write 9.24 × 105 as 92.4 × 104.
Distributive Property
Rewrite in scientific notation.= 9.929 × 105
= (6.89 × 104) + (92.4 × 104)
= 99.29 × 104 Add 6.89 and 92.4.

12. Answer
Need Another Example?
Evaluate (2.85 × 107) + (1.61 × 109). Express
the result in scientific notation.
1.6385 × 109

13. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
4. Evaluate the expression. Express the result in scientific notation.
(7.83 × 108) – 11,610,000
(7.83 × 108) – (1.161 × 107)
= (78.3 × 107) – (1.161 × 107)
Rewrite 11,610,000 in scientific
notation.
Write 7.83 × 108 as 78.3 × 107.
Subtract 1.161 from 78.3.= 77.139 × 107
= (78.3 – 1.161) × 107 Distributive Property
(7.83 × 108) – (1.161 × 107)
Rewrite in scientific notation.= 7.7139 × 108

14. Answer
Need Another Example?
Evaluate (8.23 × 106) – 391,000. Express the
result in scientific notation.
7.839 × 106

15. 1
Need Another Example?
2
3
4
Step-by-Step Example
5. 593,000 + (7.89 × 106)
= (0.593 × 106) + (7.89 × 106)
= (5.93 × 105) + (7.89 × 106) Rewrite 593,000 in scientific notation.
Write 5.93 × 105 as 0.593 × 106
Add 0.593 and 7.89.= 8.483 × 106
= (0.593 + 7.89) × 106 Distributive Property
593,000 + (7.89 × 106)

16. Answer
Need Another Example?
Evaluate 6,450,000,000 – (8.27 × 107).
Express the result in scientific notation.
6.3673 × 109

17. How did what you learned
today help you answer the
WHY is it helpful to write numbers in
different ways?
Course 3, Lesson 1-7
The Number System

18. How did what you learned
today help you answer the
WHY is it helpful to write numbers in
different ways?
Course 3, Lesson 1-7
The Number System
Sample answer:
• It is much easier to multiply or divide very large or very
small numbers when they are written in scientific
notation.

19. Write a short paragraph to
describe how yesterday’s
lesson on scientific notation
helped you with today’s
lesson.
Ratios and Proportional RelationshipsThe Number System
Course 3, Lesson 1-7