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Rational and Irrational Numbers

In this worksheet, students learn to distinguish between rational and irrational numbers.

'Rational and Irrational Numbers' worksheet

Key stage:  KS 4

Curriculum topic:  Number

Curriculum subtopic:  Change Recurring Decimals into Their Corresponding Fractions and Vice Versa

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

Rational numbers are numbers which can be written as fractions in the form p/q, where p and q are integers and q is not zero:

-5, 2, ¼, ½, 0.75, 1000, 0 .....

When written as decimals, rational numbers either terminate or recur.

 

Irrational numbers are numbers which cannot be written as fractions:

√2, √5, π, 1 + √2, 3√2

When written as decimals, irrational numbers do not terminate or recur.  

They go on for ever without repeating themselves.

Is the following number rational or irrational?

 

3

Rational

Irrational

Is the following number rational or irrational?

 

π

Rational

Irrational

Is the following number rational or irrational?

 

6

Rational

Irrational

Is the following number rational or irrational?

 

¾

Rational

Irrational

Is the following number rational or irrational?

 

Rational

Irrational

Is the following number rational or irrational?

 

√9

Rational

Irrational

Is the following number rational or irrational?

 

√10

Rational

Irrational

Is the following number rational or irrational?

 

5 - √12

Rational

Irrational

Is the following number rational or irrational?

 

3√12

Rational

Irrational

Is the following number rational or irrational?

 

3√1000

Rational

Irrational

  • Question 1

Is the following number rational or irrational?

 

3

CORRECT ANSWER
Irrational
EDDIE SAYS
Cannot be written as a fraction
  • Question 2

Is the following number rational or irrational?

 

π

CORRECT ANSWER
Irrational
EDDIE SAYS
π never recurs
  • Question 3

Is the following number rational or irrational?

 

6

CORRECT ANSWER
Rational
EDDIE SAYS
6 can be written as 6/1
  • Question 4

Is the following number rational or irrational?

 

¾

CORRECT ANSWER
Rational
EDDIE SAYS
¾ is a fraction and 0.75 terminates.
  • Question 5

Is the following number rational or irrational?

 

CORRECT ANSWER
Rational
EDDIE SAYS
6¾ can be written as 27/4
  • Question 6

Is the following number rational or irrational?

 

√9

CORRECT ANSWER
Rational
EDDIE SAYS
√9 = 3 which can be written as 3/1
  • Question 7

Is the following number rational or irrational?

 

√10

CORRECT ANSWER
Irrational
EDDIE SAYS
√10 is a non recurring decimal
  • Question 8

Is the following number rational or irrational?

 

5 - √12

CORRECT ANSWER
Irrational
EDDIE SAYS
√12 is a non recurring decimal
  • Question 9

Is the following number rational or irrational?

 

3√12

CORRECT ANSWER
Irrational
EDDIE SAYS
³√12 is a non recurring decimal
  • Question 10

Is the following number rational or irrational?

 

3√1000

CORRECT ANSWER
Rational
EDDIE SAYS
³√1000 = 10 which can be written as 10/1
---- OR ----

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