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Course 3 • Chapter 1 Real Numbers 1

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Write each fraction or mixed number as a decimal.

1. 3 −

5 2. 5 −

8 3. 9 −−

20

4. 37 −−

50 5. -

11 −−

16 6. -

9 −−

32

7. 3 1 −

5 8. 4 3 −

8 9. 5 −−

33

10. -

7 −

9 11. -8 11 −−

18 12. -9 11 −−

30

Write each decimal as a fraction or mixed number in simplest form.

13. -0.8 14. 0.44 15. -1.35

16. 0. −

8 17. -1. −

5 18. 4. −−

45

19. POPULATION Refer to the table at the right.

a. Express the fraction for Asian as a decimal.

b. Find the decimal equivalent for the fraction of the population that is African American.

c. Write the fraction for Hispanic as a decimal.

20. MEASUREMENTS Use the figure at the right.

a. Write the width of the jellybean as a fraction.

b. Write the width of the jellybean as a decimal.

Lesson 1 Homework PracticeRational Numbers

Population of Florida by Race

Race Fraction of Total Population

Asian 1 −−

50

African American 4 −−

25

Hispanic 1 −

5

in. 1

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.Lesson 2 Homework PracticePowers and Exponents

Write each expression using exponents.

1. 3 � 3 � m 2. (

1 −

4 )

(

1 −

4 )

(

1 −

4 )

3. 2 � d � 5 � d � d � 5 4. p � (-9) � p � (-9) � p � q � q

5. g � (-7) � (-7) � g � h � (-7) � h 6. x � 1 −

8 � x � x � y � 1 −

8 � y � x

Evaluate each expression.

7. (-8)4 8. (

1 −

5 )

3 9.

(

-

3 −

5 )

5

10. (-2)3 + 52 11. 34 - 52 12. (-2)5 - (-2)4

13. 43 ÷ 23 14. 53 � 23 15. 17 + (-3)4

ALGEBRA Evaluate each expression.

16. r3 - s, if r = 5 and s = 4 17. m2 - n3, if m = 6 and n = 2

18. f - g4, if f = 3 and g = -5 19. (x5 - y2)2 + x3, if x = 2 and y = 8

20. Replace with <, >, or = to make a true statement: 24 42.

21. ISLANDS Florida has about 22 � 32 � 53 islands (over 10 acres). About how many islands is this?

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Simplify. Express using exponents.

1. k8 · k 2. t7 · t6 3. 2w2 · 5w2

4. 3e3 · 7e3 5. 4r4(-4r3) 6. (-3l2w3)(2lw4)

7. (-11w4)(-5w3x4) 8. (-4b6)(-b2c3) 9. (10t4v5)(3t2v5)

10. 59 −−

53 11. 3

8 −−

3 12. b

6 −−

b4

13. g15

−−

g7 14. 18v5

−−−

9v 15. 24a6

−−−

6a5

16. y6 ÷ y3 17. n19 −−

n11 18. 9521

−−−

9518

19. Simplify 55 · 63 · 810

−−−−−−−

53 · 6 · 89 .

20. BONUSES A company has set aside 107 dollars for annual employee bonuses. If the company has 104 employees and the money is divided equally among them, how much will each employee receive?

21. CAR LOANS After making a down payment, Mr. Valle will make 62 monthly payments of 63 dollars each to pay for his new car. What is the total of the monthly payments?

Lesson 3 Homework PracticeMultiply and Divide Monomials


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.Lesson 4 Homework Practice Powers of Monomials

Simplify.

1. (6t5)2 2. (4w9)4 3. (12k6)3 4. (15m8)3

5. (4d3e5)7 6. (-4r6s15)4 7. [(72)2]2 8. [(32)2]3

9. ( 3 −

5 a6b9)2 10. (4x2)3(3x6)4 11. (0.6p5)3 12.

(

1 −

5 w5x3

)

2

GEOMETRY Express the area of each square below as a monomial.

13.

9c6d

14.

14g5h9

15. MEASUREMENT In the Metric System, you would need to have (104)2 grams to equal 1 metric ton. Simplify this measurement by multiplying the exponents, then simplify by finding the actual number of grams needed to equal 1 metric ton.

16. GAMING A video-game designer is using the expression 6n3 in a program to determine points earned, where n is the game level. Simplify the expression for the n2 level.


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.Lesson 5 Homework PracticeNegative Exponents

Write each expression using a positive exponent.

1. 8−5 2. 3−9 3. z−2 4. p−4

Evaluate each expression.

5. (−6)−5 6. 8−4 7. 2−9 8. (−7)−3

Write each fraction as an expression using a negative exponent.

9. 1 −−

29 10. 1 −−

64 11. 1 −−

e5 12. 1 −−

74

Simplify. Express using positive exponents.

13. 65 −−

62 14. n−2 · n−3 15. w

3 −−−

w−1 16. k

−4 −−

k−6

17. ROADS A state highway that is 44 miles long runs parallel to a smaller country road that is 42 miles long. How many times longer than the country road is the state highway? Write the answer as a number with a positive exponent.

18. FUNDRAISERS The hospital spent 95 dollars on new medical equipment this year. Last year, they spent 97 dollars. How many times more money did they spend last year than this year?

19. MEASUREMENT 1 milligram is equal to 10−3 grams. Write this number using a positive exponent.

20. DISTANCE A long-distance runner runs 25 miles one week and 27 miles the next week. How many times farther did he run in the second week than in the first week?


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.Lesson 6 Homework PracticeScientifi c Notation

Write each number in standard form.

1. 9.03 × 102 2. 7.89 × 103 3. 4.115 × 105 4. 3.201 × 106

5. 5.1 × 10-2 6. 7.7 × 10-5 7. 3.85 × 10-4 8. 1.04 × 10-3

Write each number in scientific notation.

9. 4,400 10. 75,000 11. 69,900,000 12. 575,000,000

13. 0.084 14. 0.0099 15. 0.000000515 16. 0.0000307

17. Which number is greater: 3.5 × 104 or 2.1 × 106?

18. Which number is less: 7.2 × 107 or 9.9 × 105?

19. POPULATION The table lists the populations of five countries. List the countries from least to greatest population.

20. SOLAR SYSTEM Pluto is 3.67 × 109 miles from the Sun. Write this number in standard form.

21. MEASUREMENT One centimeter is equal to about 0.0000062 mile. Write this number in scientific notation.

22. DISASTERS In 2005, Hurricane Katrina caused over $125 billion in damage in the southern United States. Write $125 billion in scientific notation.

Country PopulationAustralia 2 × 107

Brazil 1.9 × 108

Egypt 7.7 × 107

Luxembourg 4.7 × 105

Singapore 4.4 × 106


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.Lesson 7 Homework PracticeCompute with Scientifi c Notation

Evaluate each expression. Express the result in scientific notation.

1. (7.3 × 108)(2.4 × 103) 2. 4.62 × 107 −−−−−−−

1.2 × 104

3. 8.64 × 106 −−−−−−−

4.32 × 103 4. (5.32 × 108) – (4.6 × 106)

5. (9.67 × 106) + (3.45 × 105) 6. (4.5 × 103)(1.6 × 105)

7. (2.82 × 109) + (6.3 × 107) 8. (3.64 × 106) – (2.18 × 104)

9. 2.144 × 107 −−−−−−−

3.2 × 104 10. (7.2 × 107)(1.82 × 102)

11. (9.8 × 105) – (6.7 × 103) 12. (6.98 × 105) + (1.65 × 107)

13. (2.46 × 107)(1.78 × 102) 14. 3.936 × 105 −−−−−−−

2.4 × 102

15. MARS The diameter of Mars is about 6.8 × 103 kilometers. The diameter of Earth is about 1.2763 × 104 kilometers. About how much greater is Earth’s diameter than the diameter of Mars?

16. WAREHOUSE A factory builds a new warehouse that is approximately 1.28 × 105 square feet. Later, they add on 1.13 × 103 more square feet for offices. Use scientific notation to write the total size of the new building.


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.Lesson 8 Homework PracticeRoots

Find each root.

1. √

��

36 2. -

√

��

144 3. 3

√

��

27 −−

64 4. 3

√ ��

2,744

5. ± √

��

2.25 6. ± √

��

121 −−−

289 7.

√

��

-81 −−−

100 8. ± √

��

0.0025

9. -

√

��

0.49 10. -

√

��

3.24 11. -

√

��

25 −−−

441 12. ± √

�� 361

ALGEBRA Solve each equation. Check your solution(s).

13. h2 = 121 14. 324 = a2 15. x2 = 81 −−−

169

16. 0.0196 = m2 17. √

�

y = 6 18. √

�

z = 8.4

19. GARDENING Moesha has 196 pepper plants that she wants to plant in square formation. How many pepper plants should she plant in each row?

20. RESTAURANTS A new restaurant has ordered 64 tables for its outdoor patio. If the manager arranges the tables in a square formation, how many will be in each row?

GEOMETRY The formula for the perimeter of a square is P = 4s, where s is the length of a side. Find the perimeter of each square.

21.

Area = 144 square

inches

22. Area =

81 square feet

23.

Area = 324 square

meters


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.Lesson 9 Homework PracticeEstimate Roots

Estimate to the nearest integer.

1. √

��

38 2. √

��

53 3. √

��

99 4. √

��

227

5. 3 √

��

26 6. 3 √

��

214 7. 3 √

��

80 8. 3 √

��

510

9. √

��

86.4 10. √

��

45.2 11. √

��

7 2 −

5 12.

√

��

27 3 −

8

Order from least to greatest.

13. 8, 10, √

��

61 , √

��

71 14. √

��

45 , 9, 6, √

��

63 15. √

��

50 , 7, √

��

44 , 5

ALGEBRA Estimate the solution of each equation to the nearest integer.

16. d2 = 61 17. z2 = 85 18. r2 = 3.7

19. GEOMETRY The radius of a cylinder with volume V and height

10 centimeters is approximately √

��

V −−

30 . If a can that is 10 centimeters

tall has a volume of 900 cubic centimeters, estimate its radius.

20. TRAVEL The formula s = √

��

18d can be used to find the speed s of a car in miles per hour when the car needs d feet to come to a complete stop after slamming on the brakes. If it took a car 12 feet to come to a complete stop after slamming on the brakes, estimate the speed of the car.

GEOMETRY The formula for the area of a square is A = s2, where s is the length of a side. Estimate the length of a side for each square.

21. Area =

40 square inches

22.

Area = 97 square

feet


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.Lesson 10 Homework PracticeCompare Real Numbers

Name all sets of numbers to which the real number belongs.

1. -9 2. √

��

144 3. √

��

35 4. 8 −−

11

5. 9.55 6. 5. −

3 7. 20 −−

5 8. -

√

��

44

Replace each with <, >, or = to make a true statement.

9. √

�

8 2.7 10. √

��

15 3.9 11. 5 2 −

5 √

��

30

12. 2 3 −−

10 √

��

5.29 13. √

��

9.8 3. −

1 14. 8. −

2 8 2 −

9

Order each set of numbers from least to greatest. Verify your answer by graphing on a number line.

15. √

��

10 , √

�

8 , 2.75, 2. −

8 16. 5.01, 5.0 −

1 , 5. −−

01 , √

��

26 17. -

√

��

12 , √

��

13 , -3.5, 3.5

18. ALGEBRA The geometric mean of two numbers a and b is √

��

ab . Find the geometric mean of 32 and 50.

19. ART The area of a square painting is 600 square inches. To the nearest hundredth inch, what is the perimeter of the painting?

2.7 2.8 2.9 3 3.1 3.2 5 5.1-4 -3 -2 -1 0 1 2 3 4


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