Free Printable Unit 1B Real Numbers -- Study Guide

1.

Is the following rational or irrational?

$\sqrt{12}$

a)

Rational

b)

Irrational

2.

Is the following rational or irrational?

$\sqrt{144}$

a)

Rational

b)

Irrational

3.

Is the following rational or irrational?

$\frac{5}{6}$

a)

Rational

b)

Irrational

4.

Is the following rational or irrational?

$0.89321...$

a)

Rational

b)

Irrational

5.

Is the following rational or irrational?

$3.14$

a)

Rational

b)

Irrational

6.

Is the following rational or irrational?

$0.\overline{98}$

a)

Rational

b)

Irrational

7.

Is the following rational or irrational?

$\frac{9}{\sqrt{5}}$

a)

Rational

b)

Irrational

8.

Is the following rational or irrational?

$-4\ \frac{2}{3}$

a)

Rational

b)

Irrational

9.

Is the following rational or irrational?

$\pi$

a)

Rational

b)

Irrational

10.

Is the following rational or irrational?

$\frac{5}{3\pi}$

a)

Rational

b)

Irrational

11.

Is the following rational or irrational?

$-2.\overline{59}$

a)

Rational

b)

Irrational

12.

Is the following rational or irrational?

$\sqrt{45}$

a)

Rational

b)

Irrational

13.

Is the following rational or irrational?

$0$

a)

Rational

b)

Irrational

14.

Is the following rational or irrational?

$-2\sqrt{2}$

a)

Rational

b)

Irrational

15.

Is the following rational or irrational?

$3\pi$

a)

Rational

b)

Irrational

16.

Is the following rational or irrational?

$\frac{1}{9}$

a)

Rational

b)

Irrational

17.

Estimate $\sqrt{110}$ to the nearest tenth.

a)

$10.1$

b)

$10.8$

c)

$10.5$

d)

$10.3$

18.

Which point represents $\sqrt{50}$ ?

a)

M

b)

A

c)

T

d)

H

19.

Which point represents $\sqrt{45}$ ?

a)

M

b)

A

c)

T

d)

H

20.

Which point represents $\sqrt{37}$ ?

a)

M

b)

A

c)

T

d)

H

21.

Which point represents $\sqrt{58}$ ?

a)

M

b)

A

c)

T

d)

H

22.

If you have a square with a side length of 11 in, what is the perimeter of the square?

a)

22 in

b)

121 in

c)

11 in

d)

44 in

23.

If you have a square with a side length of 11 in, what is the area of the square?

a)

22 in²

b)

121 in²

c)

11 in²

d)

44 in²

24.

If you have a cube with a side length of 11 in, what is the volume of the cube?

a)

22 in³

b)

121 in³

c)

11³ in³

d)

44 in³

25.

If you have a square with perimeter of 24 in, what is ONE side length?

a)

6 in

b)

12 in

c)

20 in

d)

4 in

26.

If you have a square with perimeter of 24 in, what is the area?

a)

96 in²

b)

576 in²

c)

36 in²

d)

48 in²

27.

If the area of a square is 81 in², what is the perimeter?

a)

9 in

b)

324 in

c)

36 in

d)

14 in

28.

If the area of a face on a cube is 81 in², what is the volume?

a)

729 in³

b)

324 in

c)

81³ in³

d)

27 in³

29.

If the volume of a cube is 27 in³, what is the side length?

a)

9 in

b)

3 in

c)

7 in

d)

14 in

30.

If the volume of a cube is 27 in³, what is the perimeter of one face?

a)

12 in

b)

3 in

c)

7 in

d)

14 in

31.

If the volume of a cube is 27 in³, what is the area of one face?

a)

12 in²

b)

3 in²

c)

9 in²

d)

14 in²

32.

Evaluate the following:

$\sqrt{361}$

a)

17

b)

1

c)

19

d)

20

33.

Evaluate the following:

$4\sqrt{144}$

a)

12

b)

16

c)

48

d)

3

34.

Evaluate the following:

$-2\sqrt{121}$

a)

22

b)

-22

c)

9

d)

-13

35.

Evaluate the following:

$-\sqrt{225}$

a)

25

b)

15

c)

-25

d)

-15

36.

Evaluate the following:

$\sqrt{\frac{16}{25}}$

a)

$\frac{8}{13}$

b)

$4.5$

c)

$\frac{4}{5}$

d)

$\frac{5}{4}$

37.

Evaluate the following:

$\sqrt{\frac{800}{8}}$

a)

$10$

b)

$100$

c)

$\frac{100}{8}$

d)

$8$

38.

Evaluate the following:

$\ ^3\sqrt{27}$

a)

$9$

b)

$3$

39.

Evaluate the following:

$\ ^3\sqrt{216}$

a)

$9$

b)

$7$

c)

$6$

d)

$72$

40.

Evaluate the following:

$\ ^3\sqrt{125}$

a)

$9$

b)

$5$

c)

$6$

d)

$42$

41.

Evaluate the following:

$\ ^3\sqrt{729}$

a)

$9$

b)

$5$

c)

$6$

d)

$243$

42.

Evaluate the following:

$\ ^3\sqrt{8}$

a)

$4$

b)

$5$

c)

$2$

d)

$3$

43.

Evaluate the following:

$\ ^3\sqrt{64}$

a)

$4$

b)

$5$

c)

$8$

d)

$32$

44.

Evaluate the following:

$\ ^3\sqrt{\frac{8}{27}}$

a)

$\frac{3}{9}$

b)

$\frac{1}{3}$

c)

$\frac{2}{3}$

d)

$\frac{3}{2}$

45.

Evaluate the following:

$\ ^3\sqrt{\frac{64}{343}}$

a)

$\frac{4}{7}$

b)

$\frac{7}{4}$

c)

$\frac{21}{114}$

d)

$\frac{8}{16}$

46.

The area of Scout's room is 400 ft². He wants to place a border along the perimeter of the room. How much border will be needed?

a)

20 ft

b)

60 ft

c)

80 ft

d)

100 ft

47.

Dax is putting border around three sides of his 100 ft² bedroom. How much border will he use?

a)

10 ft

b)

30 ft

c)

40 ft

d)

50 ft

48.

The volume of Mrs. Cheatham's cube flask holds 512 cm³ of liquid. What is the side length of the cubed flask?

a)

171 cm

b)

8 cm

c)

256 cm

d)

23 cm

49.

Zeke and Jude are getting a puppy for Christmas. The area where the dog pen will go is 256 ft². How much fence is needed to place around the perimeter of the area?

a)

16 ft

b)

64 ft

c)

48 ft

d)

120 ft

50.

Write the repeating decimal as a fraction.

$0.\overline{45}$

a)

$\frac{5}{11}$

b)

$\frac{45}{99}$

c)

$\frac{4}{9}$

d)

$\frac{5}{9}$

51.

Write the repeating decimal as a fraction.

$0.\overline{66}$

a)

$\frac{66}{99}$

b)

$\frac{6}{9}$

c)

$\frac{2}{3}$

d)

$\frac{6}{11}$

52.

Write the repeating decimal as a fraction.

$0.\overline{8}$

a)

$\frac{8}{9}$

b)

$\frac{88}{99}$

c)

$\frac{8}{11}$

d)

$\frac{9}{8}$

53.

Write the repeating decimal as a fraction.

$0.\overline{356}$

a)

$\frac{35}{6}$

b)

$\frac{356}{999}$

c)

$\frac{35}{99}$

d)

$\frac{300}{111}$

54.

What repeating decimal would result in $\frac{6}{11}$ ?

a)

$0.\overline{54}$

b)

$0.\overline{6}$

c)

$0.\overline{611}$

d)

$0.5\overline{4}$

55.

Fill in the blank with <, >, or =.

$\frac{2}{3}$ ____ $\frac{5}{8}$

a)

$<$

b)

$>$

c)

$=$

56.

Fill in the blank with <, >, or =.

$0.03$ ____ $0.003$

a)

$<$

b)

$>$

c)

$=$

57.

Fill in the blank with <, >, or =.

$1.1$ ____ $1.05$

a)

$<$

b)

$>$

c)

$=$

58.

Fill in the blank with <, >, or =.

$\frac{2}{5}$ ____ $0.44$

a)

$<$

b)

$>$

c)

$=$

59.

Fill in the blank with <, >, or =.

$-2.75$ ____ $-2.5$

a)

$<$

b)

$>$

c)

$=$

60.

Fill in the blank with <, >, or =.

$-\frac{3}{4}$ ____ $-0.75$

a)

$<$

b)

$>$

c)

$=$

61.

$\frac{3}{8},\ \frac{1}{4},\ \frac{7}{8}$ Write the numbers in order from least to greatest.

a)

$\frac{7}{8},\frac{3}{8},\ \frac{1}{4}$

b)

$\frac{1}{4},\ \frac{3}{8},\ \frac{7}{8}$

c)

$\frac{3}{8},\frac{1}{4},\frac{7}{8}$

d)

$\frac{1}{4},\frac{7}{8},\frac{3}{8}$

62.

Write the numbers in order from least to greatest. $0.44,\ \frac{3}{8},\ 0.5,\ \frac{2}{5}$

a)

$\frac{3}{8},\ \frac{2}{5},\ 0.44,\ 0.5$

b)

$0.5,\ 0.44,\ \frac{2}{5},\ \frac{3}{8}$

c)

$0.44,\ \frac{2}{5},\ \frac{3}{8},\ 0.5$

d)

$\frac{3}{8},\ 0.44,\ \frac{2}{5},\ 0.5$

63.

Write the numbers in order from least to greatest. $0.2,\ \frac{4}{15},\ 0.21,\ \frac{1}{4}$

a)

$\frac{1}{4},\ 0.21,\ 0.2,\ \frac{4}{15}$

b)

$0.2,\ 0.21,\ \frac{1}{4},\ \frac{4}{15}$

c)

$\frac{1}{4},\ 0.2,\ 0.21,\ \frac{4}{15}$

d)

$\frac{4}{15},\ \frac{1}{4},\ 0.21,\ 0.2$

64.

Write the numbers in order from least to greatest. $-2.1,\ 0.5,\ -0.5,\ \frac{5}{100}$

a)

$-2.1,\ -0.5,\ \frac{5}{100},\ 0.5$

b)

$0.5,\ \frac{5}{100},\ -0.5,\ -2.1$

c)

$\frac{5}{100},\ -2.1,\ -0.5,\ 0.5$

d)

$-2.1,\ -0.5,\ 0.5,\ \frac{5}{100}$

65.

Write the numbers in order from least to greatest. $-10,\ 2,\ -0.5,\ \frac{5}{16}$

a)

$2,\ -10,\ \frac{5}{16},\ -0.5$

b)

$2,\ \frac{5}{16},\ -0.5,\ -10$

c)

$-10,\ -0.5,\ \frac{5}{16},\ 2$

d)

$-0.5,\ -10,\ \frac{5}{16},\ 2$

Unit 1B Real Numbers -- Study Guide

Total questions: 65

Worksheet time: 33mins

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