Rational Numbers and Irrational Numbers from "summary" of NCERT Class 10 Mathematics Solutions by JagranJosh
Rational numbers are those numbers which can be expressed in the form of p/q, where p and q are integers and q is not equal to zero. These numbers can either be positive, negative, or zero. Rational numbers are closed under addition, subtraction, multiplication, and division. This means that when we add, subtract, multiply, or divide two rational numbers, we always get a rational number as the result. For example, 3/4 + 5/6 = 22/12, which is also a rational number. On the other hand, irrational numbers are those numbers which cannot be expressed in the form of p/q. These numbers are non-terminating and non-repeating decimals. Irrational numbers cannot be written as fractions and have an infinite number of decimal places without repeating. Examples of irrational numbers include π (pi) and √2 (square root of 2). These numbers cannot be expressed as a simple fraction and have an endless decimal expansion. It is important to note that rational numbers and irrational numbers together make up the set of real numbers. Real numbers consist of both rational and irrational numbers and can be represented on the number line. Rational numbers are represented as points on the number line, while irrational numbers are represented as non-ending points between rational numbers. The set of real numbers is infinite and includes all possible numbers that can be represented on a number line.- Rational numbers can be expressed as fractions, while irrational numbers cannot. Both types of numbers make up the set of real numbers, which includes all possible numbers on the number line. Understanding the difference between rational and irrational numbers is essential in mathematics and helps us solve various problems involving real numbers.
