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.

  • Apositive
  • Bnegative

Q2:

Is 𝜋 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?

  • A 1 9
  • B 3.9
  • C 7
  • D 1 3
  • E 7 2

Q5:

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

  • A 5
  • B 5 3
  • C 5
  • D 2 9
  • E 1 1 2

Q6:

Which of the following is an irrational number?

  • A 59
  • B 109.5
  • C 6 4
  • D 7 0
  • E 1 4 4 8 1

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 [ 0 , [
  • B ] , 0 [
  • C ] , 1 [
  • D ] 0 , [
  • E [ 1 , [

Q10:

A number has the infinite decimal expansion 0 . 4 5 4 4 5 4 4 4 5 4 4 4 4 5 . . . 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 2 3
  • B 7 2 3
  • C 1 1 2 5
  • D 8 2 3
  • E 1 ( 3 + 5 8 )

Q12:

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

  • A 𝑎 0 , 𝑏 0
  • B 𝑎 = 0 , 𝑏 = 0
  • C 𝑎 0 , 𝑏 = 0
  • D 𝑎 = 0 , 𝑏 0
  • E 𝑎 = 1 , 𝑏 = 0

Q13:

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

  • Afalse
  • Btrue

Q14:

Simplify 0 . 7 6 , giving your answer in the form 𝑎 𝑏 .

  • A 7 6 1 0
  • B 7 6 1 0 0
  • C 7 6 2 5
  • D 1 9 2 5
  • E 1 9 1 0 0

Q15:

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

Which of the following is a rational number?

  • A 2
  • B 5 1 2
  • C 1 7
  • D 9
  • E 1 3

Q16:

Is every integer a rational number?

  • A yes
  • B no

Q17:

Find three rational numbers lying between 1 7 and 5 6 .

  • A 9 4 2 , 3 1 4 2 , 3 5 4 2
  • B 1 8 4 2 , 2 6 4 2 , 3 6 4 2
  • C 6 4 2 , 2 0 4 2 , 3 5 4 2
  • D 1 3 4 2 , 2 8 4 2 , 3 3 4 2

Q18:

Which of the following fractions is numerically closest to 0 . 8 2 ?

  • A 1 8 2 5
  • B 9 1 0
  • C 8 7 1 0 0
  • D 2 1 2 5
  • E 1 9 2 5

Q19:

What type of number is 1 7 3 2 ?

  • Apositive rational
  • Binteger
  • Cnegative rational

Q20:

Given that 𝑐 and 1 3 𝑐 | 𝑐 | 1 5 , what are the possible values of 𝑐 ?

  • A 1 3 , 1 3
  • B13
  • C0
  • D 1 5 , 1 5

Q21:

Find the rational number that equals 4 5 and the sum of its numerator and denominator equals 36.

  • A 8 2 8
  • B 2 0 1 6
  • C 2 0 2 5
  • D 1 6 2 0
  • E 2 8 8

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