MathsFreePrintable

Rational and Irrational Numbers Worksheet

A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Download now

Name:Date:

Rational and Irrational Numbers Worksheet

Classify each number and explain your reasoning. A rational number can be written as a fraction of integers; an irrational number has a decimal expansion that neither terminates nor repeats. Give exact answers unless asked for an approximation.

Classify the evidence

A science team is checking values for a model. Help sort its numbers into rational and irrational values.

1.Which statement best defines a rational number?

A number that is positive
A number that can be written as a fraction a/b, where a and b are integers and b ≠ 0
A number with a decimal point
A number that cannot be written exactly

2.A sensor records 0.272727… . Is this value rational or irrational? Explain what the decimal pattern tells you.

3.Choose the irrational number from the list.

√49
−3.6
√11
5/8

4.Place −1, √2, 1.5, and √5 in the correct positions on the number line. Write each label above its position.

Test the claims

Carefully check each argument. A decimal point alone does not decide whether a number is rational or irrational.

5.True or false: Every terminating decimal is rational. Give one example to support your answer.

TrueFalse

6.Complete both statements: (a) √36 is because . (b) √37 is because .

7.Match each number to its classification: 4/9, π, −12, √3, 0.125.

4/9
π
−12
√3
0.125

Irrational
Rational
Irrational
Rational
Rational

8.A student says, “0.101001000100001… is rational because it is made from the digits 0 and 1.” Explain why the reasoning is incorrect and classify the number, assuming the pattern continues by adding one more zero between each pair of 1s.

9.A square display has an area of 20 m². Write its exact side length and classify that length as rational or irrational. Then give its approximate length to two decimal places.

10.A calculator displays √5 as 2.2360679. Can this finite display prove that √5 is rational? Explain what the display does and does not show.