CBSE Class 6 Maths Notes Chapter 1: Real Numbers By Pratap Sanjay Sir
R = Real Numbers:
All rational and irrational numbers are called real numbers.
I = Integers:
All numbers from (…-3, -2, -1, 0, 1, 2, 3…) are called integers.
Q = Rational Numbers:
Real numbers of the form pq, q ≠ 0, p, q ∈ I are rational numbers.
All integers can be expressed as rational, for example, 5 = 5/1.
Decimal expansion of rational numbers can be terminating or non-terminating recurring.
Q' = Irrational Numbers:
Real numbers which cannot be expressed in the form pq and whose decimal expansions are non-terminating and non-recurring.
Roots of primes like √2, √3, √5, etc. are irrational.
N = Natural Numbers:
Counting numbers are called natural numbers. N = {1, 2, 3, …}
W = Whole Numbers:
Zero along with all natural numbers are together called whole numbers. {0, 1, 2, 3,…}
Even Numbers:
Natural numbers of the form 2n are called even numbers. (2, 4, 6, …)
Odd Numbers:
Natural numbers of the form 2n - 1 are called odd numbers. {1, 3, 5, …}
Remember this!
- All Natural Numbers are whole numbers.
- All Whole Numbers are Integers.
- All Integers are Rational Numbers.
- All Rational Numbers are Real Numbers.
Prime Numbers:
The natural numbers greater than 1 which are divisible by 1 and the number itself are called prime numbers. Prime numbers have only two factors i.e., 1 and the number itself. For example, 2, 3, 5, 7 & 11, etc.
1 is not a prime number as it has only one factor.
Composite Numbers:
The natural numbers which are divisible by 1, itself, and any other number or numbers are called composite numbers. For example, 4, 6, 8, 9, 10, etc.
Note: 1 is neither prime nor a composite number.
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