Introduction to Real Numbers Video Lecture - Class 10

Ans. Real numbers are a set of numbers that include both rational numbers (numbers that can be expressed as the quotient or fraction of two integers) and irrational numbers (numbers that cannot be expressed as fractions and have non-terminating and non-repeating decimal representations). Real numbers are represented on the number line.

Ans. Real numbers include both rational and irrational numbers, whereas rational numbers consist only of numbers that can be expressed as fractions. Real numbers are more inclusive and cover a wider range of numbers.

Ans. Yes, an example of an irrational number is the square root of 2 (√2). It cannot be expressed as a fraction and its decimal representation is non-terminating and non-repeating.

Ans. The properties of real numbers include closure, commutativity, associativity, distributivity, identity, and inverse. Closure means that the sum, difference, product, or quotient of any two real numbers will also be a real number. Commutativity states that the order of addition or multiplication does not affect the result. Associativity means that the grouping of numbers in addition or multiplication does not affect the result. Distributivity states that multiplication distributes over addition. Identity refers to the existence of an additive identity (0) and a multiplicative identity (1). Inverse means that every real number has an additive inverse and a multiplicative inverse.

Ans. Real numbers can be represented on a number line where each point corresponds to a unique real number. The positive numbers are represented on the right side of 0, while the negative numbers are represented on the left side. The distance between any two points on the number line represents the difference between the corresponding real numbers. This representation helps in visualizing the order and magnitude of real numbers.