Worksheet: Rational and Irrational Numbers

In this worksheet, we will practice identifying and telling the difference between rational and irrational numbers.

Q1:

Is 𝜋 a rational or an irrational number?

  • Aan irrational number
  • Ba rational number

Q2:

What type of number is 32?

  • ARational
  • BInteger
  • CIrrational

Q3:

Is 0.4 a rational or an irrational number?

  • Aa rational number
  • Ban irrational number

Q4:

All integers are numbers.

  • Arational
  • Birrational

Q5:

I have a number that cannot be expressed in the form 𝑎𝑏 where 𝑎, 𝑏 and 𝑏0. Is this number rational or irrational?

  • Airrational number
  • Brational number

Q6:

Is 7 a rational or an irrational number?

  • Aan irrational number
  • Ba rational number

Q7:

Is 12 a rational or an irrational number?

  • Aa rational number
  • Ban irrational number

Q8:

According to the US Mint, the diameter of a quarter is 0.955 inches. The circumference of the quarter would be the diameter multiplied by 𝜋. Is the circumference of a quarter a whole number, a rational number, or an irrational number?

  • Arational number
  • Birrational number
  • Cwhole number

Q9:

What type of number is 12? Select all that apply.

  • Ainteger
  • Brational
  • Cirrational

Q10:

What type of number is 2? Select all that apply.

  • Airrational
  • Binteger
  • Crational

Q11:

Is 2 a rational or an irrational number?

  • Aa rational number
  • Ban irrational number

Q12:

What type of number is 𝜋? Select all that apply.

  • Arational
  • Binteger
  • Cirrational

Q13:

Is 𝑒 a rational or an irrational number?

  • Aan irrational number
  • Ba rational number

Q14:

Is 0.456 a rational or an irrational number?

  • Aan irrational number
  • Ba rational number

Q15:

Without using a calculator, order the numbers 4𝜋, 43, 𝜋,12 and 34 from smallest to largest.

  • A 4 𝜋 , 3 4 , 4 3 , 𝜋 , 12
  • B 4 𝜋 , 4 3 , 3 4 , 𝜋 , 12
  • C 4 𝜋 , 4 3 , 3 4 , 12, 𝜋
  • D12, 𝜋, 43, 34, 4𝜋
  • E 3 4 , 4 3 , 𝜋 , 12, 4𝜋

Q16:

Without using a calculator, order the numbers 8, 7, and 66 from smallest to largest.

  • A 8 , 6 6 , 7
  • B 6 6 , 8 , 7
  • C 7 , 6 6 , 8
  • D 7 , 8 , 6 6
  • E 6 6 , 7 , 8

Q17:

On the number line, which arrow represents the value of 𝜋?

  • Ab
  • Bc
  • Ca

Q18:

Benjamin wants to estimate the value of 𝜋. He knows that 𝜋 is 3.14 to two decimal places but decides to round this to the nearest whole number to make this estimate easier to calculate.

What will his estimate of 𝜋 be?

Benjamin wants to check whether his approximation is accurate to the nearest whole number, so he rounds 𝜋 to 3.1. What will his approximation of 𝜋 be now?

Hence, what is an approximation of 𝜋 accurate to the nearest whole number?

Q19:

Without using a calculator, order the numbers 𝜋, 2, 1, 2, and 3 from smallest to largest.

  • A 𝜋 , 3 , 2, 2, 1
  • B1, 2, 2, 3, 𝜋
  • C1, 2, 3, 2, 𝜋
  • D 2 , 1, 3, 2, 𝜋
  • E 𝜋 , 2, 3, 2, 1

Q20:

If a rational number is not a perfect square, will its square root be rational or irrational?

  • Arational
  • Birrational
  • CIt could be either.

Q21:

What is ?

  • A
  • B
  • C { 0 }
  • D

Q22:

What is ?

  • A
  • B { 0 }
  • C
  • D

Q23:

Which of the following is an irrational number that lies between 2 and 3?

  • A 3
  • B 5 2
  • C2.6
  • D 7
  • E 1 0

Q24:

A square of side length 𝑥 cm has an area of 280 cm2. Which of the following is true about 𝑥?

  • AIt is an integer number.
  • BIt is an irrational number.
  • CIt is a negative number.
  • DIt is a natural number.
  • EIt is a rational number.

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