Worksheet: Real Numbers

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 𝜋3 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
  • B19
  • C13
  • D72
  • E7

Q5:

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

  • A5
  • B53
  • C112
  • D29
  • E5

Q6:

Which of the following is an irrational number?

  • A70
  • B64
  • C59
  • D14481
  • E109.5

Q7:

Use or to complete the following:𝜋.

  • A
  • B

Q8:

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

  • A(,0]
  • B(,0)
  • C(0,)

Q9:

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

  • A(,1)
  • B[0,)
  • C(,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
  • D1(3+58)
  • E2

Q12:

Which of the following statements must be true, given that 𝑎𝑏 is a rational number and 𝑎𝑏=0?

  • A𝑎=1, 𝑏=0
  • B𝑎0, 𝑏0
  • C𝑎=0, 𝑏=0
  • D𝑎=0, 𝑏0
  • E𝑎0, 𝑏=0

Q13:

True or False? The quotient 𝑝𝑞 where 𝑝 is an integer and 𝑞 is zero is a rational number.

  • Afalse
  • Btrue

Q14:

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

Which of the following is a rational number?

  • A17
  • B13
  • C9
  • D2
  • 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 1732?

  • Apositive rational
  • Binteger
  • Cnegative rational

Q18:

Given that 𝑐 and 13𝑐|𝑐|15, what are the possible values of 𝑐?

  • A13,13
  • B0
  • C15,15
  • 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?

  • A
  • B
  • C
  • D
  • E

Q21:

Which of the following is a pair of rational numbers which lie between 1625 and 1113?

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

Q22:

Which of the following is an irrational number?

  • A9
  • B25
  • C85
  • D50

Q23:

If 𝑥, which of the following sets contains 9𝑥?

  • A
  • B

Q24:

State whether the following is true or false: If 𝑎 and 𝑏 belong to , where 0>𝑎>𝑏, then 𝑎>𝑏.

  • Afalse
  • Btrue

Q25:

What is ?

  • A
  • B
  • C
  • D

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