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 πœ‹3 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√19
  • C√13
  • D72
  • E√7

Q5:

Which of the following is an irrational number that lies between βˆ’7 and βˆ’3?

  • Aβˆ’5
  • Bβˆ’βˆš53
  • Cβˆ’112
  • Dβˆ’βˆš29
  • Eβˆ’βˆš5

Q6:

Which of the following is an irrational number?

  • A√70
  • B√64
  • C59
  • Dο„ž14481
  • E109.5

Q7:

Use ∈ or βˆ‰ to complete the following:πœ‹β„.

  • Aβˆ‰
  • B∈

Q8:

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

  • A(βˆ’βˆž,0]
  • B(βˆ’βˆž,0)
  • C(0,∞)

Q9:

Write the interval representing the set of the positive real numbers β„οŠ°.

  • A(βˆ’βˆž,βˆ’1)
  • B[0,∞)
  • C(βˆ’βˆž,0)
  • D(0,∞)
  • E[1,∞)

Q10:

A number has the infinite decimal expansion 0.45445444544445... 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?

  • A7
  • B8
  • C11
  • Dβˆ’1(3+5βˆ’8)
  • Eο€»βˆš2ο‡οŠ©

Q12:

Which of the following statements must be true, given that π‘Žπ‘ is a rational number and π‘Žπ‘=0?

  • Aπ‘Ž=1, 𝑏=0
  • Bπ‘Žβ‰ 0, 𝑏≠0
  • Cπ‘Ž=0, 𝑏=0
  • Dπ‘Ž=0, 𝑏≠0
  • Eπ‘Žβ‰ 0, 𝑏=0

Q13:

True or False: The quotient π‘π‘ž, where 𝑝 is an integer and π‘ž is zero, is a rational number.

  • AFalse
  • BTrue

Q14:

A rational number is a number that can be written in the form π‘Žπ‘, where π‘Ž and 𝑏 are integers (whole numbers) and 𝑏 is not zero.

Which of the following is a rational number?

  • A1√7
  • Bβˆ’1√3
  • C√9
  • D√2
  • E5

Q15:

Is every integer a rational number?

  • ANo
  • BYes

Q16:

Find three rational numbers lying between 17 and 56.

  • A642,2042,3542
  • B942,3142,3542
  • C1342,2842,3342
  • D1842,2642,3642

Q17:

What type of number is βˆ’1732?

  • Apositive rational
  • Binteger
  • Cnegative rational

Q18:

Given that π‘βˆˆβ„š and 13𝑐|𝑐|βˆ’15βˆ‰β„š, what are the possible values of 𝑐?

  • A13,βˆ’13
  • B0
  • C15,βˆ’15
  • D13

Q19:

Find the rational number that equals 45 and the sum of its numerator and denominator equals 36.

  • A288
  • B828
  • C2016
  • D2025
  • E1620

Q20:

What is the union of the rational and irrational numbers?

  • Aβ„šβ€²
  • Bβ„•
  • Cβ„š
  • Dβ„€
  • Eℝ

Q21:

Which of the following is a pair of rational numbers which lie between ο„ž1625 and 1113?

  • A1213, 1
  • B85, 95
  • C1, 65
  • D5365, 5465

Q22:

Which of the following is an irrational number?

  • Aβˆ’9
  • B√25
  • C85
  • D√50

Q23:

If π‘₯βˆˆβ„οŠ±, which of the following sets contains 9π‘₯?

  • Aβ„οŠ±
  • Bβ„οŠ°

Q24:

True or False: If π‘Ž and 𝑏 belong to ℝ, where 0>π‘Ž>𝑏, then π‘Ž>π‘οŠ¨οŠ¨.

  • AFalse
  • BTrue

Q25:

What is β„šβˆͺβ„šβ€²?

  • Aβ„€
  • Bβ„š
  • Cℝ
  • Dβ„•

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