Let’s go through each number one by one and decide if it’s rational (R) or irrational (I).
Remember:
- A
rational number can be written as a fraction of two integers (like 1/2, -3/4, 5, etc.), or as a decimal that either ends or repeats.
- An
irrational number cannot be written as a simple fraction — its decimal goes on forever without repeating (like √2 or π).
---
1.
0.8 → Already done:
R (it’s 8/10, which is a fraction)
2.
–3/10 → This is already a fraction of two integers →
R
3.
√40 → Let’s simplify: √40 = √(4×10) = 2√10. Since √10 is not a perfect square, this is irrational →
I
4.
√81 → 81 is a perfect square (9×9), so √81 = 9 →
R
5.
2 1/3 → This is a mixed number, equals 7/3 → fraction of integers →
R
6.
0.35 → Terminating decimal → can be written as 35/100 →
R
7.
0.33333... → Repeating decimal → equals 1/3 →
R
8.
–9 → Integer → can be written as –9/1 →
R
9.
3.4 → Terminating decimal → 34/10 →
R
10.
√2 → Famous irrational number — decimal never ends or repeats →
I
---
Final Answer:
–3/10 → R
√40 → I
√81 → R
2 1/3 → R
0.35 → R
0.33333... → R
–9 → R
3.4 → R
√2 → I
Parent Tip: Review the logic above to help your child master the concept of identify rational numbers worksheet.
