Free Printable The Real Number System

1.

Classify the number 3

a)

Natural, Whole, Integer, Rational

b)

Whole, Rational

c)

Integer

d)

Rational

2.

How can -7.5 best be classified?

a)

rational, real

b)

irrational, real

c)

rational

d)

irrational

3.

-14 could be classified as all of these EXCEPT?

a)

Integer

b)

Real

c)

Rational

d)

Whole

4.

Classify the following number:
1.01011011101111....

a)

Rational

b)

Irrational

5.

All whole numbers are integers.

a)

False

b)

True

6.

Which statement is true?

a)

Every rational number is an integer

b)

Every whole number is a counting number

c)

Every integer is a whole number

d)

Every whole number is a rational number

7.

Classify the Number: 120

a)

Counting, whole, integers rational, real

b)

Irrational, real

c)

whole

d)

Whole, counting

8.

Classify 0

a)

Whole

b)

Integer

c)

Rational

d)

All of the above

9.

Explain the error(s).

a)

-1.2 isn't an integer.

b)

-2 isn't a whole number and 3.4 isn't a rational number.

c)

-2 isn't a whole number and -1.2 isn't an integer.

d)

The numbers are graphed correctly.

10.

A repeating decimal or decimal that terminates is called a

a)

Natural Number

b)

Irrational Number

c)

Rational Number

d)

Whole Number

11.

Natural numbers are:

a)

1.5, 2, 2.5, 3, . . .

b)

0,1,2,3,4,5...

c)

1, 2, 3, 4, . . .

d)

. . . , -2, -1, 0, 1, 2, . . .

12.

a)

A

b)

B

c)

C

d)

D

e)

E

13.

TRUE OR FALSE, the number (-10) is a whole number AND an integer.

a)

True

b)

False

14.

Estimate √50. Round your answer to the nearest Whole Number.

a)

5

b)

10

c)

25

d)

7

15.

Is √2 Irrational?

a)

Yes

b)

No

16.

What is the ONLY difference between natural numbers and whole numbers?

a)

Negative Numbers

b)

Zero

c)

Fractions

d)

Decimals

17.

The following numbers are displayed below

$\sqrt{81}$ and 9

Which value is greater?

a)

$\sqrt{81}$

b)

It cannot be determined

c)

They are equivalent

d)

9

18.

What is the square root of 16 plus the square root of 81?

a)

13

b)

The square root of 97

c)

25

d)

5

19.

Is √2 Irrational?

a)

Yes

b)

No

20.

Between which two whole numbers is the
√20 ?

a)

5 and 6

b)

10 and 2

c)

4 and 5

d)

3 and 4

21.

Will the Broncos win this weekend??

a)

Yes!!

b)

NO!!!

22.

−10 + 16 = (a)

23.

3 − 24 = (a)

24.

−15 + (−11) = (a)

25.

−8 ⋅ −9 = (a)

26.

$\frac{-57}{3}$ = (a)

27.

$\left|-14\right|$ = (a)

28.

$\left|15\right|-\left|-9\right|$ = (a)

29.

$\left|-13+2\right|$ = (a)

30.

$\left|7-\left(-10\right)\right|$ = (a)

31.

Convert $\frac{37}{50}$ to a decimal:

(a)

32.

Convert $4\%$ to a fraction (in simplest form):

(a)

33.

Answer in simplest firm:

$-1\frac{3}{4}+1\frac{1}{6}$ =

(a)

34.

Answer in simplest firm:

$-5\frac{1}{12}-3\frac{2}{3}$ =

a)

$-1\ \frac{1}{2}$

b)

$-20\ \frac{1}{6}$

c)

$-9\ \frac{1}{6}$

d)

$-1\ \frac{5}{6}$

35.

Answer in simplest firm:

$2\frac{1}{3}-\left(-4\frac{5}{6}\right)$ =

a)

$-\frac{14}{29}$

b)

$-11\ \frac{5}{18}$

c)

$7\ \frac{1}{6}$

d)

$-2\ \frac{1}{2}$

36.

Answer in simplest firm:

$\frac{2}{5}\cdot-\frac{1}{6}$ =

a)

$-2\ \frac{2}{5}$

b)

$-\frac{1}{15}$

c)

$\frac{17}{30}$

d)

$\frac{7}{30}$

37.

Answer in simplest form:

$1\ \frac{1}{2}\ \div\ 8$

a)

$\frac{3}{16}$

b)

$12$

c)

$-6\ \frac{1}{2}$

d)

$9\ \frac{1}{2}$

38.

Answer in simplest form:

$-3\ \frac{4}{7}\ \div\ -1\ \frac{1}{14}$

a)

$3\ \frac{1}{3}$

b)

$3\ \frac{81}{98}$

c)

$-2\ \frac{1}{2}$

d)

$-4\ \frac{9}{14}$

39.

Melissa ran $6\ \frac{2}{5}$ miles north, $2\ \frac{3}{4}$ west, and $2\ \frac{1}{3}$ miles south. How far did she run?

a)

$\frac{384}{385}$ miles

b)

$41\ \frac{1}{15}$ miles

c)

$1\ \frac{19}{60}$ miles

d)

$11\ \frac{29}{60}$ miles

40.

At the beginning of his diet, Jack weighed $240\ \frac{4}{5}$ pounds. At the end of the diet, he weighed $\frac{3}{4}$ his original weight. What did Jack weigh at the end of the diet?

a)

$321\ \frac{1}{15}$ lbs

b)

$180\ \frac{3}{5}$ lbs

c)

$240\ \frac{1}{20}$ lbs

d)

$241\ \frac{11}{20}$ lbs

41.

A brownie recipe calls for $1\ \frac{2}{3}$ cups of sugar. If you are making $1\ \frac{1}{2}$ times the recipe, how much more sugar will you need?

a)

$\frac{5}{9}$ more cups

b)

$\frac{5}{6}$ more cups

c)

$1\ \frac{1}{2}$ more cups

42.

Rewrite using positive exponents. **Simplify if possible.

$a^0b^{-3}c^{-1}$ =

a)

$ab^3c^1$

b)

$\frac{1}{b^3c}$ more cups

c)

$\frac{a}{b^3c}$

d)

$\frac{1}{ab^3c}$

43.

$\left(-2\right)^4\cdot\left(-6\right)^3$ =

(a)

44.

Answer in simplest form:

$\left(\frac{3}{10}\right)^3\cdot20^2$ =

(a)

45.

Rewrite using positive exponents. **Simplify if possible.

$2^{-5}$ =

(a)

46.

Rewrite using positive exponents. **Simplify if possible.

$8^{-2}\cdot6^3$ =

(a)

47.

Find each square root. **Round to the nearest tenth if neccesary.

$\sqrt[]{289}$ =

(a)

48.

Find each square root. **Round to the nearest tenth if neccesary.

$-\sqrt[]{16}$ =

(a)

49.

Find the square root. **Round to the nearest tenth if neccesary.

$-\sqrt[]{90}$ =

(a)

50.

Find each square root. **Write as a simplified fraction.

$\sqrt[]{\frac{4}{81}}$ =

(a)

51.

Identify the two consecutive integers in which the square root lies between:

$\sqrt[]{18}$

a)

2 and 3

b)

3 and 4

c)

4 and 5

d)

5 and 6

52.

Identify the two consecutive integers in which the square root lies between:

$\sqrt[]{360}$

a)

18 and 19

b)

19 and 20

c)

20 and 21

d)

21 and 22

53.

Identify the two consecutive integers in which the square root lies between:

$-\sqrt[]{195}$

a)

-10 an -11

b)

-11 and -12

c)

-12 and -13

d)

-13 and -14

54.

Write in scientific notation:

$5,028$

a)

$50.28\ \times\ 10^2$

b)

$5.028\ \times\ 10^3$

c)

$502.8\ \times\ 10$

d)

$5.028\ \times10\ ^{-3}$

55.

Find the cube root:

$\sqrt[3]{-27}$

(a)

56.

Find the cube root:

$\sqrt[3]{2744}$

(a)

57.

Write each value in scientific notation:

$0.000000216\$

a)

$2.16\ \times\ 10^{-7}$

b)

$2.16\ \times\ 10^7$

58.

Write in standard form:

$9.7\ \times\ 10^{-2}$

(a)

59.

Write in standard form:

$3.42\ \times\ 10^5$

(a)

60.

Order from least to greatest:

$2^9,\ 5.9\times10^2,\ 9^3,\ 5^4,\ 6.81\times10^1$

a)

$6.81\times10^1$

b)

$2^9$

c)

$5.9\times10^2$

d)

$5^4$

e)

$9^3$

1)

2)

3)

4)

5)

61.

Order from greatest to least:

$\sqrt[]{10},\ \frac{1}{3},\ 3\%,\ 2^{-2},\ 3.4\times10^{-2}$

a)

$\sqrt[]{10}$

b)

$\frac{1}{3}$

c)

$2^{-2}$

d)

$3.4\times10^{-2}$

e)

$3\%$

1)

2)

3)

4)

5)

62.

Solve using the Order of Operations:

$\left(19-7\right)^2-12\div3\left(2\right)$

(a)

63.

Solve using the Order of Operations:

$14-\left(3^4-\sqrt[3]{125}\right)\div4$

(a)

64.

Solve using the Order of Operations:

$3\left(5-\left|-24\right|\right)-\left(\sqrt[]{361}+2^6\right)$

(a)

65.

Solve using the Order of Operations:

$\frac{27-\left(3^2-2\cdot5\right)}{8-6^2}$

(a)

66.

Evaluate the expression given the variable replacements:

$8xy-7y^2$

if $x=-2$ and $y=-4$

(a)

67.

Evaluate the expression given the variable replacements:

$\frac{3}{2}a-ab+1$

if $a=\frac{5}{6}$ and $b=\frac{3}{10}$

(a)

68.

Name the SMALLEST SUBSET that contains the value:

$-\sqrt[]{256}$

a)

Irrational

b)

Rational

c)

Integer

d)

Whole

e)

Natural

69.

Name the SMALLEST SUBSET that contains the value:

$5^{-1}$

a)

Irrational

b)

Rational

c)

Integer

d)

Whole

e)

Natural

70.

Name the SMALLEST SUBSET that contains the value:

$\sqrt[]{88}$

a)

Irrational

b)

Rational

c)

Integer

d)

Whole

e)

Natural

71.

Name the SMALLEST SUBSET that contains the value:

$\left|-27\right|$

a)

Irrational

b)

Rational

c)

Integer

d)

Whole

e)

Natural

72.

Name the SMALLEST SUBSET that contains the value:

$1\ \frac{9}{23}$

a)

Irrational

b)

Rational

c)

Integer

d)

Whole

e)

Natural

73.

Name the SMALLEST SUBSET that contains the value:

$\sqrt[]{0}$

a)

Irrational

b)

Rational

c)

Integer

d)

Whole

e)

Natural

74.

Natural numbers are _________ integers.

a)

Always

b)

Sometimes

c)

Never

75.

Negative numbers are _________ whole numbers.

a)

Always

b)

Sometimes

c)

Never

76.

Square roots are _________ rational numbers.

a)

Always

b)

Sometimes

c)

Never

77.

Name the property that justifies the statement.

$\left(-9+2\right)\cdot0=0$

a)

Zero Product Property

b)

Associative Property of Multiplication

c)

Additive Identity

d)

Distributive Property

e)

Commutative Property

78.

Name the property that justifies the statement.

$15+0=15$

a)

Zero Product Property

b)

Associative Property

c)

Additive Identity

d)

Distributive Property

e)

Commutative Property

79.

Name the property that justifies the statement.

$15+0=15$

a)

Zero Product Property

b)

Associative Property

c)

Additive Identity

d)

Distributive Property

e)

Commutative Property

80.

Name the property that justifies the statement.

$6\left(x+7\right)=6x+42$

a)

Zero Product Property

b)

Associative Property

c)

Additive Identity

d)

Distributive Property

e)

Commutative Property

81.

Name the property that justifies the statement.

$4+\left(3+11\right)=4+\left(11+3\right)$

a)

Zero Product Property

b)

Associative Property

c)

Additive Identity

d)

Distributive Property

e)

Commutative Property

82.

Name the property that justifies the statement.

$\frac{1}{2}\cdot2=1$

a)

Zero Product Property

b)

Associative Property

c)

Additive Identity

d)

Distributive Property

e)

Multiplicative Inverse

83.

What is the additive inverse of $\left(-2m\right)$ ?

(a)

84.

What is the multiplicative identity of $\frac{4}{5}$ ?

(a)

85.

What is the additive identity of $-9$ ?

(a)

86.

What is the multiplicative inverse of $\frac{2}{3}$ ?

(a)

The Real Number System

Total questions: 86

Worksheet time: 21hrs 32mins

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