Real Numbers: Definition, Properties, and Applications

Question 1

Which of the following is NOT a real number?

Accepted Answer

π

Answer

0.25

Answer

3

Answer

−12

Question 2

Which of the following is an irrational number?

Accepted Answer

π

Answer

−5

Answer

0.5

Answer

1/3

Question 3

Which of the following real numbers is the greatest?

Accepted Answer

1

Answer

−2

Answer

0

Answer

−1

Question 4

Which of the following real numbers is the least?

Accepted Answer

−2

Answer

0

Answer

1

Answer

−1

Question 5

Which of the following is NOT a real number?

Accepted Answer

pi

Answer

0

Answer

1.414

Answer

the square root of 2

Question 6

What is the opposite of -5?

Accepted Answer

5

Answer

-5

Answer

0

Answer

10

Question 7

Which of the following is the smallest negative number?

Accepted Answer

-4

Answer

-1

Answer

-2

Answer

-3

Question 8

What is the absolute value of -7?

Accepted Answer

7

Answer

0

Answer

1

Answer

-7

Question 9

Which of the following is a closed interval?

Accepted Answer

[0, 1]

Answer

(0, 1)

Answer

(0, 1]

Answer

[0, 1)

Question 10

Which of the following is NOT a subset of real numbers?

Accepted Answer

Complex numbers

Answer

Integers

Answer

Rational numbers

Answer

Irrational numbers

Question 11

Which of the following is a rational number?

Accepted Answer

0.125

Answer

√3

Answer

e

Answer

π

Question 12

Simplify the radical expression: √(16/9)

Accepted Answer

4/3

Answer

4

Answer

3/4

Answer

16/9

Question 13

Which of the following is an example of an irrational number?

Accepted Answer

√5

Answer

1/2

Answer

-3

Answer

0.75

Question 14

What is the definition of real numbers, and why are they important in the number system?

Accepted Answer

Real numbers are all numbers that can be represented on a number line.

Answer

Real numbers are all numbers that can be expressed as a fraction of two integers.

Answer

Real numbers are all numbers that are not imaginary numbers.

Question 15

Which of the following is the smallest non-negative integer?

Accepted Answer

0

Answer

-1

Answer

1

Answer

2

Question 16

Which of the following is the reciprocal of 1/2?

Accepted Answer

2

Answer

1/4

Answer

1/2

Answer

4

Question 17

Which of the following is the greatest common divisor (GCD) of 12 and 18?

Accepted Answer

3

Answer

2

Answer

6

Answer

9

Question 18

Which of the following is the slope of the line passing through the points (1, 2) and (3, 8)?

Accepted Answer

4

Answer

2

Answer

3

Answer

6

Question 19

Which of the following is a rational number?

Accepted Answer

5/7

Answer

0.1234567...

Answer

-√3

Answer

e

Question 20

Which of the following is an irrational number?

Accepted Answer

π

Answer

-2

Answer

0.5

Answer

√16

Question 21

Which of the following is equivalent to -(-5)?

Accepted Answer

5

Answer

-5

Answer

0

Answer

|5|

Question 22

Which property guarantees that every non-empty set of real numbers with an upper bound also has a least upper bound?

Accepted Answer

Completeness Property

Answer

Associative Property

Answer

Distributive Property

Answer

Commutative Property

Question 23

Which of the following is an example of an irrational number, a non-terminating and non-repeating decimal?

Accepted Answer

√2

Answer

-5

Answer

3/4

Answer

0.25

Question 24

A patient's weight fluctuated by -2.3 pounds over a week. What does the negative sign signify?

Accepted Answer

The patient lost weight.

Answer

Weight cannot be negative.

Answer

The weight measurement is incorrect.

Answer

The patient gained weight.

Question 25

Which property is exemplified by the equation: 5 + (7 + 3) = (5 + 7) + 3?

Accepted Answer

Associative Property of Addition

Answer

Commutative Property of Addition

Answer

Distributive Property

Answer

Identity Property of Addition

Question 26

Which number is the smallest?

Accepted Answer

-3.5

Answer

√2

Answer

0

Answer

-1.2

Question 27

Express the rational number 5/8 as a decimal.

Accepted Answer

0.625

Answer

5.8

Answer

0.58

Answer

1.6

Question 28

In scientific notation, what is the dosage of a medication given as 0.025 mg/kg?

Accepted Answer

2.5 x 10^-2 mg/kg

Answer

0.25 x 10^-1 mg/kg

Answer

2.5 x 10^2 mg/kg

Answer

25 x 10^-3 mg/kg

Question 29

Which set consists exclusively of rational numbers?

Accepted Answer

{ -7, 0, 1/2, 2.5 }

Answer

{ -7, π, 1/2, 2.5 }

Answer

{ -7, 0, √3, 2.5 }

Answer

{ -√2, 0, 1/2, 2.5 }

Question 30

Determine the absolute value of -5.8.

Accepted Answer

5.8

Answer

-0.8

Answer

0.8

Answer

-5.8

Question 31

A patient's blood pressure decreased by 15% from 120/80 mmHg. Calculate the new systolic pressure.

Accepted Answer

120 - (0.15 x 120)

Answer

120 + (0.15 x 120)

Answer

120 / 0.15

Answer

120 x 0.15

Question 32

Which of the following is a rational number?

Accepted Answer

1/2

Answer

√2

Answer

π

Answer

0

Question 33

Which of the following numbers is an integer?

Accepted Answer

-5

Answer

0

Answer

1.5

Answer

√3

Question 34

Which of the following is an irrational number?

Accepted Answer

√2

Answer

0

Answer

-5

Answer

1/2

Question 35

What is the additive inverse of -1?

Accepted Answer

1

Answer

0

Answer

-0.5

Answer

2

Question 36

Which of these is the smallest positive integer?

Accepted Answer

1

Answer

-1

Answer

0

Answer

2

Question 37

Which of the following is the largest negative integer?

Accepted Answer

-1

Answer

-2

Answer

0

Answer

1

Question 38

Which decimal is equivalent to the fraction 1/2?

Accepted Answer

0.5

Answer

0.75

Answer

1.5

Answer

0.25

Question 39

What is the value of -√4?

Accepted Answer

-2

Answer

-4

Answer

4

Answer

2

Question 40

Which of the following is NOT a real number?

Accepted Answer

Imaginary number

Answer

Integer

Answer

Irrational number

Answer

Rational number

Question 41

What is the result of (-5)²?

Accepted Answer

25

Answer

10

Answer

-25

Answer

-10

Question 42

What is the decimal representation of the rational number 2/5?

Accepted Answer

0.4

Answer

0.2

Answer

0.5

Answer

0.6

Question 43

Find the square root of 169.

Accepted Answer

13

Answer

12

Answer

14

Answer

15

Question 44

Determine the inequality that corresponds to the set of all real numbers greater than or equal to -2 and less than 5.

Accepted Answer

-2 ≤ x < 5

Answer

-2 < x ≤ 5

Answer

x > -2 and x < 5

Answer

x ≥ -2 and x ≤ 5

Question 45

Find the multiplicative inverse of 3/4.

Accepted Answer

4/3

Answer

-4/3

Answer

-3/4

Answer

3/4

Question 46

Identify the smallest negative integer.

Accepted Answer

-1

Answer

-3

Answer

-2

Answer

-4

Question 47

Convert the repeating decimal 0.333... into its decimal equivalent.

Accepted Answer

1/3

Answer

2/3

Answer

3/3

Answer

4/3

Question 48

Classify the set of real numbers that are not rational.

Accepted Answer

Irrational numbers

Answer

Integers

Answer

Rational numbers

Question 49

Which of the following is an irrational number?

Accepted Answer

√2

Answer

1/3

Answer

-5

Question 50

What is the decimal representation of the rational number 3/4?

Accepted Answer

0.75

Answer

0.43

Answer

0.34

Question 51

Which of the following properties is NOT true for real numbers?

Accepted Answer

Division by zero is always possible.

Answer

Addition is commutative.

Answer

Multiplication is associative.

Question 52

What is the absolute value of -7?

Accepted Answer

7

Answer

14

Answer

0

Answer

-7

Question 53

Which of the following numbers is an integer but not a natural number?

Accepted Answer

-3

Answer

10

Answer

5

Answer

1

Question 54

If x is a real number, what is the solution to the inequality x > 3?

Accepted Answer

All real numbers greater than 3

Answer

All real numbers less than 3

Answer

Only the number 3

Question 55

Which of the following numbers is the largest?

Accepted Answer

√16

Answer

3.5

Answer

π

Question 56

The number line represents all ____ numbers.

Accepted Answer

real

Answer

integer

Answer

natural

Answer

rational

Question 57

What is the result of adding a positive and a negative number?

Accepted Answer

The result depends on the magnitude of each number.

Answer

Always positive

Answer

Always negative

Question 58

Which of the following is NOT a property of the additive identity (0)?

Accepted Answer

It is the only number that can be multiplied by any real number to get zero.

Answer

Adding zero to any real number does not change the number.

Answer

Zero is its own additive inverse.