ML Aggarwal Solutions for Class 9 Maths Chapter 1 Rational And Irrational Numbers

A rational number is a number that can be express as the ratio of two integers. A number that cannot be expressed that way is irrational. However, numbers like √2 are irrational because it is impossible to express √2 as a ratio of two integers. Rational numbers are numbers that can be expressed as a fraction or part of a whole number. (Examples: -7, 2/3, 3.75) Irrational numbers are numbers that cannot be expressed as a fraction or ratio of two integers. There is no finite way to express them. (Examples: √2, π, e).

Rational Numbers • Any number which can be put in the form of p/q where p and q are integers and q not equal to zero is called a rational number. • There exist an infinite number of rational numbers between any two rational numbers • For example, in between 7 and 7.5, there exist 7.1, 7.11, 7.21, etc.) • A fraction is a rational number only when it is in its lowest form, i.e., there is no common factor other than 1 in the numerator (p) and denominator (q) Irrational Numbers Those numbers which cannot be expressed in the form of pq where p,q are integers and q not equal to zero are called irrational numbers. The sum, difference, product or quotient of two irrational numbers may not be an irrational number. Negative of an irrational number is also an irrational number.

Examples are 1.8632457……..,2–√ etc.