Class-9 : Maths - Chapter-1. Number Systems. ( Ex-1.1, Ex-1.2, Ex-1.3, Ex-1.4, Ex-1.5, Ex-1.6)

Points to Remember 

• Natural numbers are : 1, 2, 3, …………….. denoted by N.

• Whole numbers are : 0, 1, 2, 3, ……………… denoted by W.

• Integers : ……. -3, -2, -1, 0, 1, 2, 3, ……………… denoted by Z.

• Rational numbers : The numbers which can be written in the form of p/q , where p and q are integers and q≠0 . Every integer p is also a rational number, can be written as p/1.

• Irrational numbers - A number is called irrational, if it cannot be written in the form of p/q, where p and q are integers and q≠0.

• Terminating decimals: The rational numbers with a finite decimal part or for which the long division terminates after a finite number of steps are known as finite or terminating decimals.

• Non-Terminating decimals: The rational numbers with an infinite decimal part or for which the long division does not terminate even after an infinite number of steps are known as infinite or non-terminating decimals.

• Real numbers: All the rational numbers and irrational numbers taken together make a collection of real numbers. Hence, it is either rational or irrational.

• If A is rational and B is irrational then A+B, A–B, A.B are always irrational numbers but A/B may be rational or irrational.

• We can locate √n for any positive integer n on number line, after √(n-1) is located. 

• Rationalization: It means to remove square root from the denominator by multiplying it's numerator & denominator by a suitable number.

Exercise - 1.1

Exercise - 1.2

Exercise - 1.3

Exercise - 1.4

Exercise - 1.5

Exercise - 1.6

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