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

Q5:

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

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

Q6:

Which of the following is an irrational number?

  • A 7 0
  • B 6 4
  • C59
  • D 1 4 4 8 1
  • 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?

  • A 7
  • B 8
  • C 1 1
  • D 1 ( 3 + 5 8 )
  • E 2

Q12:

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

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

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

Q15:

Is every integer a rational number?

  • Ano
  • Byes

Q16:

Find three rational numbers lying between 17 and 56.

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

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?

  • A 1 3 , 1 3
  • B0
  • C 1 5 , 1 5
  • D13

Q19:

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

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

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?

  • A 1 2 1 3 , 1
  • B 8 5 , 9 5
  • C1, 65
  • D 5 3 6 5 , 5 4 6 5

Q22:

Which of the following is an irrational number?

  • A 9
  • B 2 5
  • C 8 5
  • D 5 0

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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