📘 Class 9 Maths – Homework
🧮 Topic: Classify Numbers
In Mathematics, numbers are classified into various types based on their properties.
- Natural Numbers (\( \mathbb{N} \)) – Counting numbers: 1, 2, 3, …
- Whole Numbers (\( \mathbb{W} \)) – Natural numbers + 0: 0, 1, 2, 3, …
- Integers (\( \mathbb{Z} \)) – Positive & negative whole numbers: -3, -2, 0, 1, 2, …
- Rational Numbers (\( \mathbb{Q} \)) – Numbers in form \( \frac{p}{q} \), \( q \ne 0 \)
- Irrational Numbers – Numbers that cannot be expressed as \( \frac{p}{q} \): √2, π
- Real Numbers (\( \mathbb{R} \)) – Combination of Rational and Irrational numbers
📌 Solved Examples
🔹 Classify \( \sqrt{16} \):
\( \sqrt{16} = 4 \), which is a Natural, Whole, Integer, Rational, Real number ✅
\( \sqrt{16} = 4 \), which is a Natural, Whole, Integer, Rational, Real number ✅
🔹 Classify \( -5 \):
Integer, Rational, Real ✅
Integer, Rational, Real ✅
🔹 Classify \( \frac{7}{2} \):
Rational, Real ✅
Rational, Real ✅
🔹 Classify \( \pi \):
Irrational, Real ✅
Irrational, Real ✅
🔹 Classify 0:
Whole, Integer, Rational, Real ✅
Whole, Integer, Rational, Real ✅
📚 Homework Worksheet – With Answers
Below are the answers for the classification of the given numbers:
| # | Number | Correct Classification |
|---|---|---|
| 1️⃣ | \( \sqrt{25} \) | Natural, Whole, Integer, Rational, Real |
| 2️⃣ | \( -8 \) | Integer, Rational, Real |
| 3️⃣ | \( \frac{2}{7} \) | Rational, Real |
| 4️⃣ | \( \pi \) | Irrational, Real |
| 5️⃣ | \( 0 \) | Whole, Integer, Rational, Real |
| 6️⃣ | \( 14 \) | Natural, Whole, Integer, Rational, Real |
| 7️⃣ | \( -\frac{5}{3} \) | Rational, Real |
| 8️⃣ | \( \sqrt{2} \) | Irrational, Real |
| 9️⃣ | \( 9.5 \) | Rational, Real |
| 🔟 | \( -1 \) | Integer, Rational, Real |
📝 Tip: You can double-check by expressing the numbers in decimal or fraction forms and comparing with their definitions!