Number System

• Classification of Number

  • Natural Numbers(N)- 1, 2, 3, 4, 5...... (Also called counting no.s)
  • Whole Numbers(W)- 0, 1, 2, 3, 4, 5.....

  ->All Natural numbers including zero are called Whole Numbers.

  -> Every Natural number is a Whole number, but NOT vice-versa.
• Classification of Number

  • All Natural numbers, Whole numbers, negative numbers and 0 are called Integers.
  • Integers(Z)- (....-3, -2, -1, 0, 1, 2, 3....)

  -> Zero is neither positive nor negative.

  A) Integers

  
• Classification of Numbers

  • Rational Numbers

  
• Classification of Numbers

  • Irrational Numbers or Non-rational Numbers

  -> Though not ALL square roots are irrational....

  eg:- √25 = 5, √4 = 2, √64 = 8....(rational numbers)

  
• Classification of Numbers

  • All Natural numbers, Whole numbers, and Integers are Rational Numbers, but NOT vice-versa.
  • Rational numbers and Irrational numbers, together are called Real Numbers.

  
• Real Numbers and Decimal Expansion

  
• Decimal Expansion

  Q) Express 3.3333... in p/q form.

  A) Decimal Expansion in p/q form

  
• A SIMPLE TRICK

  To change decimal expansion to p/q form.

  -> Only works for decimals having 0 before the decimal point and when ALL the numbers are being repeated past the decimal point.

  -> Only to be used for 1 marker type questions.

  
• Operations on Rational Numbers

  -> 'Not defined' means that the result is neither Rational nor Irrational, it is NOT POSSIBLE!

  
• Operations in Irrational Numbers

  -> In addition and subtraction of two Irrationals the outcome will be Irrational.

  -> But in multiplication or division, the outcome may or may not be irrational.

  
• ALGEBRAIC IDENTITIES

  Important Rules to be kept in mind.

  
• Rationalize the Denominator

  => { √a x √a = a }

  
• Rationalize the Denominator

  Example Que 1.

  
• Rationalize the Denominator

  Example Que 2.

  
• Laws of Exponents

  =>  (2)6 [Raised to the power 6]

  • Base = 2
  • Exponent/Power =6