Classify Real Numbers

Classify Real Numbers

All numbers on the number line (a line representing the set of all real numbers) are referred as real numbers. The number line is typically marked showing integer values. Real numbers includes positives and negatives numbers, integers and rational numbers, square roots, cube roots, π (pi), etc. Real numbers are indicated by R. Complex numbers that are not real numbers. That is, the complex numbers with a nontrivial imaginary part. For example, 4 + 3i is non-real, 3i is non-real, but 4 is real.

Classify Real Numbers - Classify Numbers

Natural Number (N) – Non-negative numbers from 1; N = {1, 2, 3, 4, 5...}.

Whole Number (W) – Non-negative numbers from 0; W = {0, 1, 2, 3...}

Integer (Z) – Positive and negative numbers; Z = {…-3, -2, -1, 0, 1, 2, 3…}

Rational Number (Q) – Ratio or quotient of an integer and another non-zero integer; Q = {n/m | n, m ∈ Z, m ≠ 0}. Example: -50, -20(1/4), -1.5, 0, 1.5, 2(2/3).

Irrational Number – Numbers which cannot be represented as fractions; √2, √5, π

Real Number (R) – All the numbers on a number line. Union of all rational and irrational numbers.

Imaginary number – Number which square is a negative real number; -5i, 7.5i

Complex Number (C) – Number consist of real and imaginary part; a + bi

I like to share this list of all the prime numbers with you all through my article.

Classify Real Numbers – Examples

Example 1: Classify real Numbers

a) 1/3 b) 11 c) √14 d) 5i e) -5

Solution:

a) 1/ 3 is in the form of a/b, b ≠ 0

When dividing 1 by 3 we get 0.333… (Repeating decimal)

Therefore 1/3 is a rational number.

b) 11 is a whole, natural, integer, rational number.

11/1 = 11.0, so 11 is terminating decimal.

c) √14 is an irrational number

d) 5i is a imaginary number

e) -5 is a integer number

Example 2: Multiply these complex numbers (4 + i) (4 – i)

Solution:

= (4 + i) (4 + i) = (16 + 4i + 4i + i^2)

= (16 + 8i - 1) = (15 + 8i)                (i^2 = -1)

Example 3: Multiply (4 – 5) (3 – i^4)

Solution:

(4 – 5) (3 – i^4) = (12 – 4i^4 - 15 + 5i^4)

= (12 – 4(1) – 15 + 5(1) = (12 – 4 – 15 + 5) = -2