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Rational Irrational Numbers Worksheet

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Rational Irrational Numbers Worksheet

Classify numbers using exact values, not just calculator displays. A rational number can be written as a/b, where a and b are integers and b ≠ 0. Its decimal terminates or repeats. An irrational number has a decimal that neither terminates nor repeats. Show working where asked.

At the maths festival

A maths festival is setting up puzzle stations about number types. Help the organisers check their number cards.

1.A station needs a card showing a rational number. Which one should the organiser choose?

√11
0.375
π
√13

2.Classify each number as rational (R) or irrational (I). Give one brief reason for each classification: √36, 0.121212…, √10, −7/9, and π.

3.A display places numbers from least to greatest. Use the number line to order −1.5, −√2, 0, and √2.

4.True or false? Every terminating decimal is rational. Explain your choice using 0.625 as an example.

Check the reasoning

The organisers are testing explanations before they print the station signs.

5.A student says, “0.272727… is irrational because its digits go on forever.” Is the student correct? Explain and write the decimal as a fraction.

6.Explain why √49 is rational but √50 is irrational.

7.Which two cards show irrational numbers? Select both.

−2.4
√64
√6
π/3

8.Complete the number-card table. Write R or I in the final column.

Number

Reason or exact value

R or I

−12

5/6

√81

√3 + 2

0.1010010001…

9.A calculator shows √2 ≈ 1.41421. Why does this display not prove that √2 is rational?

10.A puzzle asks for an irrational number between 4 and 5. Give one example and justify why it fits.

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Rational Irrational Numbers Worksheet

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At the maths festival

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3 printable pages

About This Worksheet

Free in Kuraplan

Print-Ready

AI-Generated

For Teachers & Parents

Need a custom version of this worksheet?

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