📘 Real Numbers Class 10 Notes (Chapter 1) – Complete Explanation

🔷 Introduction to Real Numbers

Real Numbers are a fundamental concept in mathematics that include different types of numbers such as natural numbers, whole numbers, integers, rational numbers, and irrational numbers. These concepts are essential for building a strong foundation in Class 10 Maths.

🔹 1. Natural Numbers

Natural numbers are the counting numbers that start from 1 and go to infinity.

Examples:
1, 2, 3, 4, 5, …

👉 These are used for counting objects.

🔹 2. Whole Numbers

Whole numbers include all natural numbers along with zero.

Examples:
0, 1, 2, 3, 4, …

👉 Whole numbers start from 0 and extend to infinity.

🔹 3. Integers

Integers include all positive numbers, negative numbers, and zero.

Examples:
-3, -2, -1, 0, 1, 2, 3

👉 Used in situations like temperature, profit/loss, etc.

🔹 4. Odd Numbers

Odd numbers are numbers that are not divisible by 2.

Examples:
1, 3, 5, 7, …

🔹 5. Even Numbers

Even numbers are numbers that are divisible by 2.

Examples:
2, 4, 6, 8, …

🔹 6. Rational Numbers

Rational numbers are numbers that can be written in the form:$$\frac{p}{q}, \quad \text{where } p, q \text{ are integers and } q \neq 0$$qp​,where p,q are integers and q=0

Examples:
-2, -1, 0, 1/2, 5, -5

👉 Key Property:
There are infinitely many rational numbers between any two numbers.

Formula to find a rational number between a and b:$$\frac{a + b}{2}$$2a+b​

🔹 7. Irrational Numbers

Irrational numbers are numbers that cannot be written in the form of p/q.

Examples:
√2, √3, √5, π

👉 Their decimal expansion is non-terminating and non-repeating.

🔹 Important Concept

✔ Square root of any prime number is always an irrational number.

🔹 8. Prime Numbers

Prime numbers are numbers that have only two factors: 1 and itself.

Examples:
2, 3, 5, 7, 11, …

👉 Smallest prime number = 2

🔹 Prime Number Facts

• Prime numbers between 1 to 50 → 15
• Prime numbers between 51 to 100 → 10
• Total prime numbers between 1 to 100 → 25