1. Course 3, Lesson 1-2
Write each fraction or mixed number as a decimal.
1. 2. 3.
Write each decimal as a fraction or mixed number in
simplest form.
4. 0.08 5. 1.375
6. The largest moth is the Atlas moth. The Atlas moth is
11.8 inches long. What is the length of an Atlas moth
written as a mixed number?
7
8
5
12
3
2
20

2. Course3, Lesson 1-2
ANSWERS
1. 0.875
2.
3. 2.15
4.
5.
6.
0.416
2
25
3
1
8
4
11 in.
5

3. WHY is it helpful to write numbers in
different ways?
The Number System
Course3, Lesson 1-2

4. Course3, Lesson 1-2 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.1
Know and apply the properties of integer exponents to generate
equivalent numerical expressions.
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.
8 Look for and express regularity in repeated reasoning.

5. • To write and evaluate
expressions using exponents
Course3, Lesson 1-2
The Number System

6. • power
• base
• exponent
Course3, Lesson 1-2
The Number System

7. 1
Need Another Example?
2
Step-by-Step Example
1. Write the expression using exponents.
(–2) • (–2) • (–2) • 3 • 3 • 3 • 3
The base –2 is a factor 3 times, and the base 3
is a factor 4 times.
(–2) • (–2) • (–2) • 3 • 3 • 3 • 3 = (–2)3 • 34

8. Answer
Need Another Example?
Write (–9) • (–9) • (–9) • (–9) • (–9) • 4 • 4 • 4 as
an expression using exponents.
(–9)5 • 43

9. 1
Need Another Example?
2
3
Step-by-Step Example
2. Write the expression using exponents.
a • b • b • a • b
Use the properties of operations to rewrite and group
like bases together. The base a is a factor 2 times,
and the base b is a factor 3 times.
a • b • b • a • b = a • a • b • b • b
= a2 • b3

10. Answer
Need Another Example?
Write x • y • x • y • x • x as an expression
using exponents.
x4 • y2

11. 1
Need Another Example?
2
Step-by-Step Example
3. Evaluate .
=
Write the power as a product.
Multiply

12. Answer
Need Another Example?
Evaluate .

13. 1
Need Another Example?
2
3
4
Step-by-Step Example
4. The deck of a skateboard has an area of about
25 • 7 square inches. What is the area of the
skateboard deck?
25 • 7 = 2 • 2 • 2 • 2 • 2 • 7 Write the power as a product.
Associative Property= (2 • 2 • 2 • 2 • 2) • 7
= 32 • 7 or 224
The area of the skateboard deck is about
224 square inches.
Multiply.

14. Answer
Need Another Example?
A racquetball court has an area of 2 • 42 • 52
square feet. What is the area of the
racquetball court?
800 ft2

15. 1
Need Another Example?
2
3
Step-by-Step Example
5. Evaluate the expression if a = 3 and b = 5.
a2 + b4
a2 + b4 = 32 + 54 Replace a with 3 and b with 5.
Write the powers as products.= (3 • 3) + (5 • 5 • 5 • 5)
= 9 + 625 or 634 Add.

16. Answer
Need Another Example?
Evaluate x3 + y5 if x = 4 and y = 2.
96

17. 1
Need Another Example?
2
3
Step-by-Step Example
6. Evaluate the expression if a = 3 and b = 5.
(a – b)2
(a – b)2 = (3 – 5)2 Replace a with 3 and b with 5.
Perform operations in the
parentheses first.
= (–2)2
= (–2) • (–2) or 4
Write the powers as products.
Then simplify.

18. Answer
Need Another Example?
Evaluate (x + y)2 if x = 4 and y = 2.
36

19. How did what you learned
today help you answer the
WHY is it helpful to write numbers in
different ways?
Course 3, Lesson 1-2
The Number System

20. How did what you learned
today help you answer the
WHY is it helpful to write numbers in
different ways?
Course 3, Lesson 1-2
The Number System
Sample answers:
• Writing numbers using powers is a short way of writing
very large numbers.
• You would use exponents when you work with the
metric system since the metric system is based on
powers of ten.

21. Write about how you think
powers and exponents
connect with multiplying
and dividing monomials.
Ratios and Proportional RelationshipsThe Number System
Course 3, Lesson 1-2