Let's classify each number as
Rational (R) or
Irrational (I). A
rational number can be expressed as a fraction of two integers (where the denominator is not zero), and its decimal form either terminates or repeats. An
irrational number cannot be written as a simple fraction, and its decimal goes on forever without repeating.
---
Step-by-step classification:
1.
0.8 → Already given as
R
- This is a terminating decimal → can be written as $ \frac{4}{5} $ → Rational
2.
$-\frac{3}{10}$
- This is already a fraction of two integers → Rational
→
R
3.
$\sqrt{40}$
- $ \sqrt{40} = \sqrt{4 \times 10} = 2\sqrt{10} $
- $ \sqrt{10} $ is irrational → so $ \sqrt{40} $ is irrational
→
I
4.
$\sqrt{81}$
- $ \sqrt{81} = 9 $ → which is an integer → Rational
→
R
5.
$2\frac{1}{3}$
- This is a mixed number: $ 2 + \frac{1}{3} = \frac{7}{3} $ → fraction of integers → Rational
→
R
6.
0.35
- Terminating decimal → can be written as $ \frac{35}{100} = \frac{7}{20} $ → Rational
→
R
7.
0.3333...
- Repeating decimal → this is $ \frac{1}{3} $ → Rational
→
R
8.
−9
- Integer → can be written as $ \frac{-9}{1} $ → Rational
→
R
9.
3.4
- Terminating decimal → $ \frac{34}{10} = \frac{17}{5} $ → Rational
→
R
10.
$\sqrt{2}$
- Well-known irrational number → cannot be expressed as a fraction, non-repeating, non-terminating decimal
→
I
---
Final Answer Table:
| Number | Rational or Irrational? |
|---------------|--------------------------|
| 0.8 | R |
| $-\frac{3}{10}$ | R |
| $\sqrt{40}$ | I |
| $\sqrt{81}$ | R |
| $2\frac{1}{3}$ | R |
| 0.35 | R |
| 0.3333... | R |
| −9 | R |
| 3.4 | R |
| $\sqrt{2}$ | I |
✔ All classified!
Parent Tip: Review the logic above to help your child master the concept of identifying rational numbers worksheet.
