Ch-1 Rational And Irrational Numbers Ex-1(C) Q. No.6-16 From Selina Concise For ICSE Class 9 Math

#rationalandirrational #icseclass9maths #icsemaths #maths #math #mathematics #jindalmathspoint #selinasolutions#ch_1_rationalandirrational
Rational and irrational numbers are two different types of real numbers in mathematics.

Rational Numbers:

Rational numbers are numbers that can be expressed as a ratio or fraction of two integers, where the denominator is not zero.
They can be written in the form a/b, where a and b are integers, and b is not equal to zero.
Examples of rational numbers include 1/2, -3/4, 5, 0, and any integer.
Irrational Numbers:

Irrational numbers are numbers that cannot be expressed as a simple fraction or ratio of two integers.
They have non-repeating, non-terminating decimal expansions.
Examples of irrational numbers include the square root of 2 (√2), pi (π), and Euler's number (e).
Here are some key differences between rational and irrational numbers:

Representation: Rational numbers can be represented as fractions or ratios of integers, while irrational numbers cannot be represented in this way.

Decimal Expansion: Rational numbers always have finite or repeating decimal expansions, whereas irrational numbers have non-repeating, non-terminating decimal expansions.

Examples: Most integers and fractions are rational numbers, while famous mathematical constants like √2, π, and e are irrational numbers.

Density: There are an infinite number of both rational and irrational numbers, but between any two distinct rational numbers, there are infinitely many irrational numbers.

Operations: When you add, subtract, multiply, or divide two rational numbers, the result is always a rational number. However, performing these operations on irrational numbers may result in either rational or irrational numbers.

Approximations: Irrational numbers are often approximated as decimals or fractions for practical calculations because their exact values cannot be expressed. For instance, π is often approximated as 3.14159, which is a rational approximation.

Understanding the distinction between rational and irrational numbers is fundamental in mathematics, especially in real analysis, algebra, and calculus, where these types of numbers are used extensively.
for online tuitions contact me at 7009509669
thanks for watching @jindalmathspoint

Видео Ch-1 Rational And Irrational Numbers Ex-1(C) Q. No.6-16 From Selina Concise For ICSE Class 9 Math канала Jindal Maths Point