Learn essential real number formulas Class 10. Understand key concepts and master formulas of real numbers class 10 for exam success.
Number Systems
- Natural Numbers (N): N = {1, 2, 3, 4, 5, …} (All counting numbers).
- Whole Numbers (W): W = {0, 1, 2, 3, 4, 5, …} (All natural numbers + 0).
- Integers (Z): Z = {…, -3, -2, -1, 0, 1, 2, 3, …}
- Positive Integers (Z+): {1, 2, 3, 4, …}
- Negative Integers (Z–): {…, -4, -3, -2, -1}
Rational Numbers
If a number can be expressed in the form p/q, where q ≠ 0 and p, q are integers, it is a rational number. Examples: 1/2, (-3)/2, 8/(-7).
Irrational Numbers
If a number cannot be expressed in the form p/q, where q ≠ 0 and p, q are integers, it is an irrational number. Examples: √2, √3, √5.
Real Numbers (R)
The set of real numbers includes all natural numbers (N), whole numbers (W), integers (Z), rational numbers, and irrational numbers.
Euclid’s Division Lemma
For any two positive integers a and b, there exist unique integers q (quotient) and r (remainder) such that:
a = bq + r, where 0 ≤ r < b.
- a: Dividend
- b: Divisor
- q: Quotient
- r: Remainder
HCF (Highest Common Factor)
The Highest Common Factor (HCF) of two given positive integers is the largest positive integer that divides them.
Use Euclid’s Division Algorithm to find the HCF.
Fundamental Theorem of Arithmetic
Express every composite number as a unique product of prime numbers, apart from the order of the primes.
Formula: HCF(a, b) × LCM(a, b) = a × b
Important Concept for Rational Numbers
A rational number has a terminating decimal expansion if it can be expressed in the form:
p / (2n × 5m), where n and m are non-negative integers.
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