# Lesson Worksheet: Real Numbers Mathematics • 8th Grade

In this worksheet, we will practice distinguishing between rational and irrational numbers and representing real numbers on number lines.

Q1:

Every natural number is a real number.

• Anegative
• Bpositive

Q2:

Is a rational or an irrational number?

• Aan irrational number
• Ba rational number

Q3:

Is 0.456 a rational or an irrational number?

• Aa rational number
• Ban irrational number

Q4:

Which of the following is an irrational number that lies between 3 and 4?

• A3.9
• B
• C
• D
• E

Q5:

Which of the following is an irrational number that lies between and ?

• A
• B
• C
• D
• E

Q6:

Which of the following is an irrational number?

• A
• B
• C59
• D
• E109.5

Q7:

Use or to complete the following:.

• A
• B

Q8:

Write the interval that represents the set of nonpositive real numbers.

• A
• B
• C

Q9:

Write the interval representing the set of the positive real numbers .

• A
• B
• C
• D
• E

Q10:

A number has the infinite decimal expansion where the number of fours between the fives continues to increase. Is this a rational number?

• Ano
• Byes

Q11:

Which of the following is a rational number?

• A
• B
• C
• D
• E

Q12:

Which of the following statements must be true, given that is a rational number and ?

• A,
• B,
• C,
• D,
• E,

Q13:

True or False: The quotient , where is an integer and is zero, is a rational number.

• AFalse
• BTrue

Q14:

A rational number is a number that can be written in the form , where and are integers (whole numbers) and is not zero.

Which of the following is a rational number?

• A
• B
• C
• D
• E

Q15:

Is every integer a rational number?

• ANo
• BYes

Q16:

Find three rational numbers lying between and .

• A
• B
• C
• D

Q17:

What type of number is ?

• Apositive rational
• Binteger
• Cnegative rational

Q18:

Given that and , what are the possible values of ?

• A
• B0
• C
• D13

Q19:

Find the rational number that equals and the sum of its numerator and denominator equals 36.

• A
• B
• C
• D
• E

Q20:

What is the union of the rational and irrational numbers?

• A
• B
• C
• D
• E

Q21:

Which of the following is a pair of rational numbers which lie between and ?

• A, 1
• B,
• C1,
• D,

Q22:

Which of the following is an irrational number?

• A
• B
• C
• D

Q23:

If , which of the following sets contains ?

• A
• B

Q24:

True or False: If and belong to , where , then .

• AFalse
• BTrue

Q25:

What is ?

• A
• B
• C
• D