📘 Class 10 Maths – Chapter 1: Real Numbers
Free Notes | BookNNotes
🔹 What are Real Numbers?
Real numbers are numbers which can be represented on a number line.
These include both rational and irrational numbers.
Real Numbers = Rational Numbers + Irrational Numbers
🔹 Types of Numbers
- Natural Numbers: 1, 2, 3, 4, ...
- Whole Numbers: 0, 1, 2, 3, ...
- Integers: -3, -2, -1, 0, 1, 2, 3
- Rational Numbers: Numbers which can be written as p/q, where q ≠ 0
- Irrational Numbers: Numbers which cannot be written as p/q (√2, √3, π)
🔹 Euclid’s Division Lemma
For any two positive integers a and b,
there exist unique integers q and r such that:
a = bq + r, where 0 ≤ r < b
Example:
If a = 17 and b = 5
Then: 17 = 5 × 3 + 2
🔹 Euclid’s Division Algorithm
Euclid’s Division Algorithm is used to find the HCF (Highest Common Factor)
of two positive integers.
Steps:
- Apply Euclid’s Division Lemma
- If remainder ≠ 0, repeat the process
- When remainder becomes 0, the divisor is the HCF
🔹 Fundamental Theorem of Arithmetic
Every composite number can be expressed as a product of primes, and this
factorization is unique (except for order).
Example:
180 = 2 × 2 × 3 × 3 × 5
🔹 Key Points to Remember
- Every rational number has either a terminating or recurring decimal expansion
- Irrational numbers have non-terminating and non-repeating decimals
- HCF can be found using Euclid’s Algorithm
📌 This was Day 1 – Chapter 1 Real Numbers
Kal next topic ya next chapter ke notes upload kar sakti hain.
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