CBSE Class 10 Maths Notes Chapter 1 Real
Numbers
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 = 51
Decimal expansion of rational numbers 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, …}
Why can’t we write the form as 2n+1?
Remember this!
All Natural Numbers are whole numbers.
All Whole Numbers are Integers.
All Integers are Rational Numbers.
All Rational Numbers are Real Numbers.
Numbers
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 = 51
Decimal expansion of rational numbers 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, …}
Why can’t we write the form as 2n+1?
Remember this!
All Natural Numbers are whole numbers.
All Whole Numbers are Integers.
All Integers are Rational Numbers.
All Rational Numbers are Real Numbers.
