Real Numbers

What are Real Numbers?

When both the rational and irrational numbers combined, the combination is defined as the real numbers. Real numbers can be both positive or negative, and they are denoted by the symbol “R”. Numbers like a natural number, decimals, and fraction comes under the real number.

Real Numbers

Classification of Real Numbers

  • Natural Numbers- It includes all the counting numbers such as 1, 2, 3, 4,…
  • Whole Numbers- Numbers starting with zero are called whole numbers, like 0, 1, 2, 3, 4,…
  • Integers- Whole numbers and negative of all natural numbers are collectively known as integers, for example -3, -2, -1, 0, 1, 2,
  • Rational Numbers- All the numbers that can be written in the form of p/q, where \(q\neq 0\) are known as Rational numbers.
  • Irrational Numbers- The numbers which cannot be written in the form of p/q (simple fraction) are known as irrational numbers. Irrational numbers are non-terminating and non-repeating in nature.

Properties of real numbers

  • Commutative property- If we have real numbers m,n. The general form will be m + n = n + m  for addition and m.n = n.m for multiplication.
  • Associative property- If we have real numbers m, n, r. The general form will be  m + (n + r) = (m + n) + r for addition(mn) r = m (nr) for multiplication
  • Distributive property- If we have real numbers m,n,r. The general form will be – m (n + r) = mn + mr and (m + n) r = mr + nr
  • Identity property- For addition: m + (- m) = 0

Solve the model questions on Real Numbers that are provided in detail through simple step-step solutions to all questions in an NCERT textbooks only at BYJU’S.

Practise This Question

The line x + y = 1 meets x - axis at A and y - axis at B. P is the mid - point of AB P1 is the foot of the perpendicular from P to OA; M1 is that from P1 to OP; P2 is that from M1 to OA; M2 is that from P2 to OP; P3 is that from M2 to OA and so on. If Pn denotes the nth foot of the perpendicular on OA from Mn1, then OPn =