Number System : Types of Numbers Video Lecture | CAT Made Easy - Video Lectures by Nishant Sir | IIM K

Ans. The number system consists of various types of numbers, including natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Natural numbers are the set of positive integers starting from 1 (1, 2, 3,...). Whole numbers include all natural numbers along with 0 (0, 1, 2, 3,...). Integers encompass all whole numbers and their negative counterparts (..., -3, -2, -1, 0, 1, 2, 3,...). Rational numbers are those that can be expressed as a fraction of two integers, where the denominator is not zero (e.g., ½, -3/4). Lastly, irrational numbers cannot be expressed as simple fractions and have non-repeating, non-terminating decimal expansions (e.g., √2, π).

Ans. Rational numbers can be expressed as the quotient of two integers (a/b), where b is not zero, and include both terminating and repeating decimals. For example, 0.75 (which is ¾) and 0.333... (which is ⅓) are rational. In contrast, irrational numbers cannot be expressed as a fraction and have decimal expansions that are neither terminating nor repeating. Examples include numbers like √2 and π, which cannot be represented as exact fractions.

Ans. Zero holds a unique position in the number system. It is classified as a whole number and an integer, but it is not considered a natural number. The significance of zero lies in its role as a placeholder in the decimal system, allowing for the representation of large numbers and enabling arithmetic operations. Additionally, zero is crucial in defining certain mathematical concepts, such as the identity element in addition (a + 0 = a) and the concept of null value in various mathematical contexts.

Ans. Rational numbers are frequently used in real life, such as in financial transactions, measurements, and statistical data. For example, when dividing a bill among friends or measuring ingredients in cooking, rational numbers come into play. On the other hand, irrational numbers are often encountered in geometry and engineering, particularly in calculations involving circles. The constant π (approximately 3.14) is used in formulas for the circumference and area of circles, while √2 appears in the diagonal length of a square with sides of unit length.

Ans. Complex numbers extend the number system beyond real numbers. They are expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit defined as the square root of -1. Complex numbers are essential in various fields such as engineering, physics, and applied mathematics, particularly in solving equations that do not have real solutions. They provide a framework for understanding phenomena like electrical circuits and waveforms, where both magnitude and phase angle are crucial.